Product Description
This book is a unique introduction to the theory of linear operators on Hilbert space.The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians.Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook. ... Read more

Customer Reviews (6)

Thorough, clear and very relevant for engineering students
At graduate school, I was required to take only 9 credit units in advanced Mathematics. Most of my credits were on Numerical Analysis, Mathematical Optimization and Linear Algebra. However, as I started covering advanced courses in dynamical systems, robust control and nonlinear systems, I found that I really needed strong foundations in Functional Analysis. I audited one course in Functional Analysis where we used the classic Rudin text. However, the pace of that class was too fast for me and I virtually learnt nothing. So I graduated with a handicap that I was unable to handle most rigorous problems. Knowing my handicap, I bought several books on this subject; I did not want to spend too much money, so each book did not cost more than $50 on Amazon marketplace. At first it was very disappointing because each book that I bought was written in the traditional format of Definition-Theorem-Proof without explaining the basic concepts. The last book to buy was this one which I read chapter by chapter from page one to the last page for about four months every evening. I believe this will be my last book on functional analysis, because it has provided what I have been looking for.

The book is well organized, and it provides detailed discussion on each topic followed with numerous and easy to understand examples that are directly related to physical systems. The reader can visualize the concepts by relating to physical systems, which is what engineering students want. After four months of evening reading, it is amazing that now I can tackle all analysis problems that used to intimidate me. This book is a must for all graduate students whose major covers dynamical systems, controls, nonlinear systems or signal processing.

Excellent applied functional analysis text
This is a great book for the applied mathematician, scientist, or engineer who wants an applicable and not overly formal introduction to functional analysis.Many examples illustrating the use of the techniques are given throughout.The text is quite readable, with a unique organization introducing algebraic, topological, and combined algebraic-topological structures and their associated theory.The book presents functional analysis without explicitly relying on the Lebesgue integral, although a well-written appendix covers Lebesgue integration and some related concepts from real variable theory.I would have appreciated more discussion of differential equations, but overall this is a very well-written book and a worthy purchase.

An eminently readable functional analysis book
An eminently readable functional analysis book including an appendix on measure theory and probability spaces. The text covers the material without explicit development of the Lebesgue integral. The notation and typesettingare very clean and the section on spectral analysis is unusually good. Theproofs are very clean and complete with numerous illustrative engineeringexamples and diagrams.I recommend this book for graduate levelengineering students.

Enlightening for mathematicians, scientists, and engineers
This is one of my favourite introductory books on functional analysis because it includes all the fundamental concepts needed to get a thorough understanding of the most important topics in this theory. It stresseswhich properties come from which structure (set-theoretic, topological, oralgebraic), and gives a complete exposition of the main results on boundedand unbounded operators, meanwhile discussing some interesting examples ofapplication. Its appendices on integration, probability and stochasticprocesses are also valuable. The text is suitable for undergraduateanalysis and functional analysis courses. Scientists and engineers willfind it very useful also because of its non-pedantic style.

Please checkmy other reviews in my member page (just click on my name above).

Continued Comment
I also recommend the "Optimizaton by vector space" by David Luenberger. It is also a very good book on linear operator with optimization applications. ... Read more

Product Description
This work and Fundamentals of the Theory of Operator Algebras. Volume II, Advanced Theory present an introduction to functional analysis and the initial fundamentals of $C^*$- and von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Major concepts are sometimes presented from several points of view; the account is leisurely when brevity would compromise clarity. An unusual feature in a text at this level is the extent to which it is self-contained; for example, it introduces all the elementary functional analysis needed. The emphasis is on teaching. Well supplied with exercises, the text assumes only basic measure theory and topology. The book presents the possibility for the design of numerous courses aimed at different audiences. ... Read more

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This advanced undergraduate- and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. 1981 ed.
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Customer Reviews (2)

Excellent overview of the material
This book is excellent. I don't pretend it should be used as a course for either quantum mechanics or functional analysis. It is at a level way above that necessary for quantum mechanics and it does not cover enough material to be a serious textbook for functional analysis.

That said at 15$ it is a great addition to any library. A reader can move through the book and really get an understanding of the topics presented. The books by Reed and Simon are a must for any mathematical physicist but they can sometimes be intimidating. The material presented here is relevant and presented in a very straightforward manner. If you have a background in analysis and wish to learn more about quantum mechanics I would definitely recommend this book. Another possible use is as an additional text in a functional analysis course so students can see direct applications.

A Unique and Interesting Book.
The book is about the mathematics of a single particle in 1-D space, the line, written for math people.Yeah, it's 300 pages for a little guy moving in a straight line!Isn't that enough?

It's about mathematical modeling, power, and beauty.Physics background is not required.Maybe no idea is even better!Prof. Schechter has spent much time preparing the contents, so you don't have to look around.

This book could be used as a first course in mathematical physics, or a supplement of mathematical modeling or functional analysis.Prof. Schechter teaches us about translating QM postulates into math.Starts off very simple 1-D case for a particle, and no more.Again, isn't that enough?

I think "encouraging" is the best word to describe his style for this book.A very gentle math teacher.The quality of math is as good as von Neumann or Weyl, and the representation is better.He even tells you what probability really is.(Do you know?)

It's more user-friendly than many other mathematical physics books.And the cover is maybe one of the most beautiful among Dover paperbacks.

Yet another "Mathematical Foundations of Quantum Mechanics" -- a very unique one!

I was very lucky to encounter this book which was almost hidden in a pile of books. Attracted by the cover design, so I pulled it out hard.Then found that I was right.

If you are kind-of math guy and interested in QM or modeling as well, check this book out.It's hard to find in bookstores, though.

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"Though this be madness, yet there's method in it." -- Polunius, in Hamlet. ... Read more

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This text discusses electromagnetics from the view of operator theory, in a manner more commonly seen in textbooks of quantum mechanics. It includes a self-contained introduction to operator theory, presenting definitions and theorems, plus proofs of the theorems when these are simple or enlightening.

Customer Reviews (1)

The missing link... at last
This book represents what I personally think is the missing link. Which link is that and between what?... well, the book introduces the reader to the very useful and easy, yet rigors theory of operators. This analytical tool is outstanding when someone wants to start proper analysis of an electromagnetic problem and wishes to do it in higher level of abstraction on the paper yet, with high level of details and physical understanding in mind. Therefore, The book is the link between the electromagnetism and theory of operators. The book is very useful for engineers and physicists who are not particularly interested in pure mathematics but instead, interested in the theory of operators as a powerful tool for both analytical and numerical formulations in electromagnetics. As a result, this book for advanced users and I suggest the beginners and intermediate readers to start with the book by Donald G. Dudley "Mathematical Foundations for Electromagnetic Theory ". Other sources that are of a great importance and support this book and make it perfect is the two by Ismo V. Lindell "Methods for Electromagnetic Field Analysis" and "Differential forms in Ellectromagnetics" ... Read more

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This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.

Product Description
The unifying theme is the Banach space duality for operator algebras, allowing readers to recognize the affinity between operator algebras and measure theory on locally compact spaces. ... Read more

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This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes.Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study.The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems.Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them. ... Read more

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Offers graduate students, mathematicians, and scientists a clear presentation of fundamental topics of operator theory. Uses a systematic presentation, covering such important concepts as set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces. DLC: Operator theory--Mathematics. ... Read more

Customer Reviews (4)

Good introduction
I enjoyed reading this book. As another reviewer said, the proofs are a little too detailed. However, for my purposes, a little hand-holding was just what I needed. I haven't read any other books on the subject, so I can't make a thorough comparison. However, I have been reading sections of Conway's "A Course In Functional Analysis". Here are some surface differences.

1. Both books have a large number of typos and other errata. Both authors provide an errata page on the web. Conway's book is in it's third printing so as expected, it has fewer errata. In any case, most of the errata are typos that are easy to spot and fix on your own.

2. The proofs in Kubrusly's book are far more detailed than Conway's. As a result, you can read it much faster, but you don't get as much out of it.

3. Conway covers much more ground than Kubrusly. Some areas that I am interested in, Banach Algebras, the Riesz functional calculus, and unbounded operators are not covered at all in Kubrusly.

I have this complaint about Professor Kubrusly's proofs. It is not always clear exactly what he is proving. If the theorem is of the 'if and only if' type, he will start his proof without telling you which half he is doing. In the proof of the Arzela-Ascoli theorem, he doesn't tell you what he is proving until two pages after he starts the proof. I suppose this is not such a big deal since eventually you do find out what he is proving.

For someone like me who wants to go deeper into the field, this book is a good introduction, but requires you to read a second book. For someone who really only needs the material that is covered in the book, you will find it a painless introduction.

A useful book, great for the beginner
This is a very self-contained book on fundamentals of functional analysis. The pace is very slow and the proofs too detailed at times. This is particularly so in Chapter 5 on Hilbert Spaces. The good thing about this book are the problems at the end of each chapter. They are mostly standard problems and a lot of 'hints' are provided (as opposed to most books in this field). I have a number of books on functional analysis but often I go back to Kubrusly's for some fundamental notion. One downside is the brief treatment on the spectral theorem for normal operators, but I guess the author's intention was too avoid using measure theoretic results, which most engineering students are not familiar with. A great pick for the engineer seeking a better understanding of higher mathematics.

Simply Indispensable
This is a must have Analisys book. Although the modest title, the book is the best introduction to functional analysis ever written. More than this, its an indispensable first book for everyone interested in operator theory. It is clear, concise and all the exercises are really solvable. You feel that the autor wants to teach you. It requires only a modest (really!) background in linear algebra and calculus. At the end, you will have learned all real analysis that so many autors (and teachers!) always have hidden from you. There are so many math disclosure in the book that I'm afraid Kubrusly being at risk of attack from any xiita math (especially the mediocre one). I agree with the last reviewer, the book is an immediate classic and Kubrusly has turned himself into a kind of Salman Rushdie for his daring in writing the Satanic Verses of the Mathematics.

It's a imediate classic!!
For those wanting to learn not only functional analisys but also the basic elements about math (set thoery, algebra, topology,...), I doubt that they can find anything better than this book. It's the state of art!!! ... Read more

Product Description
An Invitation to Operator Theory offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory. The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool. ... Read more

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Operator theory is a significant part of many important areas of modern mathematics: functional analysis, differential equations, index theory, representation theory, mathematical physics, and more. This text covers the central themes of operator theory, presented with the excellent clarity and style that readers have come to associate with Conway's writing. Early chapters introduce and review material on C*-algebras, normal operators, compact operators and non-normal operators. The topics include the spectral theorem, the functional calculus and the Fredholm index. Also, some deep connections between operator theory and analytic functions are presented. Later chapters cover more advanced topics, such as representations of C*-algebras, compact perturbations and von Neumann algebras. Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory. These advanced topics are at the heart of current research. The last chapter gives an introduction to reflexive subspaces, i.e., subspaces of operators that are determined by their invariant subspaces. These, along with hyperreflexive spaces, are one of the more successful episodes in the modern study of asymmetric algebras. Professor Conway's authoritative treatment makes this a compelling and rigorous course text, suitable for graduate students who have had a standard course in functional analysis. ... Read more

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This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.

The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed.

The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book.

The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem.

Product Description
Basic Operator Theory provides an introduction to functional analysis with an emphasis on the theory of linear operators and its application to differential and integral equations, approximation theory, and numerical analysis. A textbook designed for senior undergraduate and graduate students, Basic Operator Theory begins with the geometry of Hilbert space and proceeds to the spectral theory for compact self-adjoint operators with a wide range of applications. Part of the volume is devoted to Banach spaces and operators acting on these spaces.Presented as a natural continuation of linear algebra, Basic Operator Theory provides a firm foundation in operator theory, an essential part of mathematical training for students of mathematics, engineering, and other technical sciences. ... Read more

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Operator theory is a diverse area of mathematics which derives its impetus and motivation from several sources. It began with the study of integral equations and now includes the study of operators and collections of operators arising in various branches of physics and mechanics. The intention of this book is to discuss certain advanced topics in operator theory and to provide the necessary background for them assuming only the standard senior-first year graduate courses in general topology, measure theory, and algebra. At the end of each chapter there are source notes which suggest additional reading along with giving some comments on who proved what and when. In addition, following each chapter is a large number of problems of varying difficulty. This new edition will appeal to a new generation of students seeking an introduction to operator theory. ... Read more

Customer Reviews (1)

Disappointing
If this book is disappointing why did I rate it 5 stars? Well, it is because having studied the first edition I was expecting more updates in the second. It really is an excellent book, but I wanted the author to discuss the Brown-Douglas-Fillmore K-theory of operator algebras and give an in-depth discussion of the invariant subspace conjecture. I used this book for a two semester course in functional analysis and operator theory while a sophomore in undergraduate and found it very challenging. The presentation of the topics is very quick and the problems are pretty difficult, but you take away an appreciation of this important area of mathematics. Indeed, the theory of Hp-spaces and Toeplitz operators, which are covered in the last two chapters, have many applications in engineering and physics. The author does give an update on the problems he marked with two stars (indicating an unsolved problem) in the first edition, and references that discuss their solution. When studying the book, I am always amazed about how rich linear transformations become when they operate on infinite-dimensional Hilbert spaces; but also how much the finite-dimensional results have generalizations in infinite dimensions. The theory of C* and W*-algebras is discussed in the book, and the presentation should be helpful to physicists who use these techniques, even though the presentation is much more general than one would find in physical theories. The explanation of the W*-algebra as arising from the enlargement of the functional calculus to an algebra of functions generated by characteristic functions; where the Gelfand transform is taken on a larger commutative self-adjoint subalgebra of the space of linear operators is one that is easier to remember and seems more natural than merely giving a set of axioms that a W*-algebra is supposed to satisfy. A very abstract discussion of index theory is given, and one that is pretty distant from the theory of integral equations, but with some work one can see the connection to these equations. Who knows, maybe a third edition with more of the author's insights? ... Read more

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The study of composition operators forges links between fundamental properties of linear operators and beautiful results from the classical theory of analytic functions. This book provides a self-contained introduction to both the subject and its function-theoretic underpinnings. The development is geometrically motivated, and accessible to anyone who has studied basic graduate-level real and complex analysis. The work explores how operator-theoretic issues such as boundedness, compactness, and cyclicity evolve - in the setting of composition operators on the Hilbert space H2 into questions about subordination, value distribution, angular derivatives, iteration, and functional equations. Each of these classical topics is developed fully, and particular attention is paid to their common geometric heritage as descendants of the Schwarz Lemma. ... Read more

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This text, part of the "Springer Classics of Mathematics" series, examines perturbation theory for linear operators. ... Read more

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This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday.The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefinite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians. ... Read more

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This volume contains contributions written by participants of the 4th Workshop on Operator Theory in Krein Spaces and Applications, which was held at the TU Berlin, Germany, December 17 to 19, 2004. The workshop covered topics from spectral, perturbation and extension theory of linear operators and relations in inner product spaces, including spectral analysis of differential operators, the theory of generalized Nevanlinna functions and related classes of functions, spectral theory of matrix polynomials, and problems from scattering theory.

Product Description
The theory of dual algebras (ultraweakly closed algebras of operators on Hilbert space) has made tremendous progress since 1978, when Scott Brown originated some of the main ideas to solve the invariant subspace problem for subnormal operators. The impetus for much of this progress has come from the authors of the present book, who, in a sequence of papers, have added several new ideas concerning the solution of systems of simultaneous equations in the predual of a dual algebra, thereby developing a dilation theory and contributing substantially to the theories of invariant subspaces and reflexivity. In addition to containing the major results of the theory as presented in earlier papers by the authors and other mathematicians, this important study presents much material not previously available elsewhere. Accessible to graduate students having knowledge of a first course in operator theory, this excellent book will be of interest to all researchers in the field. ... Read more

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In this fully-illustrated textbook, the author examines thespectral theory of self-adjoint elliptic operators. Chapters focus ontheproblems of convergence and summability of spectraldecompositionsabout the fundamental functions of elliptic operatorsof the secondorder. The author's work offers a novel method forestimation of theremainder term of a spectral function and its Rieszmeans withoutrecourse to the traditional Carleman technique andTauberian theoremapparatus. ... Read more

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This volume is the companion volume to Fundamentals of the Theory of Operator Algebras. Volume I--Elementary Theory (Graduate Studies in Mathematics series, Volume 15). The goal of the text proper is to teach the subject and lead readers to where the vast literature--in the subject specifically and in its many applications--becomes accessible. The choice of material was made from among the fundamentals of what may be called the ``classical'' theory of operator algebras. This volume contains the written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume I--Elementary Theory. ... Read more