Basic Operator Theory

Author : Israel Gohberg,Seymour Goldberg
Publisher : Birkhäuser
Page : 291 pages
File Size : 54,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461259855

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Basic Operator Theory by Israel Gohberg,Seymour Goldberg Pdf

rii application of linear operators on a Hilbert space. We begin with a chapter on the geometry of Hilbert space and then proceed to the spectral theory of compact self adjoint operators; operational calculus is next presented as a nat ural outgrowth of the spectral theory. The second part of the text concentrates on Banach spaces and linear operators acting on these spaces. It includes, for example, the three 'basic principles of linear analysis and the Riesz Fredholm theory of compact operators. Both parts contain plenty of applications. All chapters deal exclusively with linear problems, except for the last chapter which is an introduction to the theory of nonlinear operators. In addition to the standard topics in functional anal ysis, we have presented relatively recent results which appear, for example, in Chapter VII. In general, in writ ing this book, the authors were strongly influenced by re cent developments in operator theory which affected the choice of topics, proofs and exercises. One of the main features of this book is the large number of new exercises chosen to expand the reader's com prehension of the material, and to train him or her in the use of it. In the beginning portion of the book we offer a large selection of computational exercises; later, the proportion of exercises dealing with theoretical questions increases. We have, however, omitted exercises after Chap ters V, VII and XII due to the specialized nature of the subject matter.

Author : Israel Gohberg,Seymour Goldberg,Marinus Kaashoek
Publisher : Birkhäuser
Page : 428 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034879804

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Basic Classes of Linear Operators by Israel Gohberg,Seymour Goldberg,Marinus Kaashoek Pdf

A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.

Author : Israel Gohberg,Seymour Goldberg
Publisher : Unknown
Page : 304 pages
File Size : 43,7 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 146125986X

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Basic Operator Theory by Israel Gohberg,Seymour Goldberg Pdf

Author : Yiśrāʿēl Z. Gohberg,Seymour Goldberg
Publisher : Unknown
Page : 285 pages
File Size : 43,6 Mb
Release : 2001
Category : Operator theory
ISBN : 3764342625

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Basic Operator Theory by Yiśrāʿēl Z. Gohberg,Seymour Goldberg Pdf

Author : Harkrishan Lal Vasudeva
Publisher : Springer
Page : 522 pages
File Size : 54,8 Mb
Release : 2017-03-27
Category : Mathematics
ISBN : 9789811030208

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Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva Pdf

The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different classes of operators, such as normal operators, self-adjoint operators, unitaries, isometries and compact operators have been discussed. A large number of examples of operators, along with their spectrum and its splitting into point spectrum, continuous spectrum, residual spectrum, approximate point spectrum and compression spectrum, have been worked out. Spectral theorems for self-adjoint operators, and normal operators, follow the spectral theorem for compact normal operators. The book also discusses invariant subspaces with special attention to the Volterra operator and unbounded operators. In order to make the text as accessible as possible, motivation for the topics is introduced and a greater amount of explanation than is usually found in standard texts on the subject is provided. The abstract theory in the book is supplemented with concrete examples. It is expected that these features will help the reader get a good grasp of the topics discussed. Hints and solutions to all the problems are collected at the end of the book. Additional features are introduced in the book when it becomes imperative. This spirit is kept alive throughout the book.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 48,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475733280

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Elements of Operator Theory by Carlos S. Kubrusly Pdf

{\it Elements of Operatory Theory} is aimed at graduate students as well as a new generation of mathematicians and scientists who need to apply operator theory to their field. Written in a user-friendly, motivating style, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, Hilbert spaces, culminating with the Spectral Theorem, one of the landmarks in the theory of operators on Hilbert spaces. The exposition is concept-driven and as much as possible avoids the formula-computational approach. Key features of this largely self-contained work include: * required background material to each chapter * fully rigorous proofs, over 300 of them, are specially tailored to the presentation and some are new * more than 100 examples and, in several cases, interesting counterexamples that demonstrate the frontiers of an important theorem * over 300 problems, many with hints * both problems and examples underscore further auxiliary results and extensions of the main theory; in this non-traditional framework, the reader is challenged and has a chance to prove the principal theorems anew This work is an excellent text for the classroom as well as a self-study resource for researchers. Prerequisites include an introduction to analysis and to functions of a complex variable, which most first-year graduate students in mathematics, engineering, or another formal science have already acquired. Measure theory and integration theory are required only for the last section of the final chapter.

Author : Reza Saadati
Publisher : Academic Press
Page : 82 pages
File Size : 41,6 Mb
Release : 2016-08-24
Category : Mathematics
ISBN : 9780081009550

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Random Operator Theory by Reza Saadati Pdf

Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equations Delves into the study of random operator theory Discusses the concept of random Banach algebras and its applications

Author : Mortad Mohammed Hichem
Publisher : World Scientific
Page : 656 pages
File Size : 53,8 Mb
Release : 2018-10-15
Category : Mathematics
ISBN : 9789813236271

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An Operator Theory Problem Book by Mortad Mohammed Hichem Pdf

This book is for third and fourth year university mathematics students (and Master students) as well as lecturers and tutors in mathematics and anyone who needs the basic facts on Operator Theory (e.g. Quantum Mechanists). The main setting for bounded linear operators here is a Hilbert space. There is, however, a generous part on General Functional Analysis (not too advanced though). There is also a chapter on Unbounded Closed Operators.The book is divided into two parts. The first part contains essential background on all of the covered topics with the sections: True or False Questions, Exercises, Tests and More Exercises. In the second part, readers may find answers and detailed solutions to the True or False Questions, Exercises and Tests.Another virtue of the book is the variety of the topics and the exercises and the way they are tackled. In many cases, the approaches are different from what is known in the literature. Also, some very recent results from research papers are included.

Author : Gerald J. Murphy
Publisher : Academic Press
Page : 297 pages
File Size : 50,8 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080924960

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C*-Algebras and Operator Theory by Gerald J. Murphy Pdf

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Author : George W. Hanson,Alexander B. Yakovlev
Publisher : Springer Science & Business Media
Page : 640 pages
File Size : 40,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9781475736793

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Operator Theory for Electromagnetics by George W. Hanson,Alexander B. Yakovlev Pdf

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.

Author : Israel Gohberg,Seymour Goldberg,M. A. Kaashoek
Publisher : Birkhauser
Page : 494 pages
File Size : 42,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015019434573

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Classes of Linear Operators by Israel Gohberg,Seymour Goldberg,M. A. Kaashoek Pdf

Author : Vladimir Müller
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 50,9 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783764382650

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Spectral Theory of Linear Operators by Vladimir Müller Pdf

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. Many results appear here for the first time in a monograph.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 53,5 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9780817649982

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The Elements of Operator Theory by Carlos S. Kubrusly Pdf

This second edition of Elements of Operator Theory is a concept-driven textbook that includes a significant expansion of the problems and solutions used to illustrate the principles of operator theory. Written in a user-friendly, motivating style intended to avoid the formula-computational approach, fundamental topics are presented in a systematic fashion, i.e., set theory, algebraic structures, topological structures, Banach spaces, and Hilbert spaces, culminating with the Spectral Theorem. Included in this edition: more than 150 examples, with several interesting counterexamples that demonstrate the frontiers of important theorems, as many as 300 fully rigorous proofs, specially tailored to the presentation, 300 problems, many with hints, and an additional 20 pages of problems for the second edition. *This self-contained work is an excellent text for the classroom as well as a self-study resource for researchers.

Author : John B. Conway
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 47,7 Mb
Release : 2000
Category : Operator theory
ISBN : 9780821820650

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A Course in Operator Theory by John B. Conway Pdf

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. Some of the major topics covered are the spectral theorem, the functional calculus, and the Fredholm index. In addition, 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. The last chapter gives an introduction to reflexive subspaces, which 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.

Author : Erik M. Alfsen,Frederik W. Shultz
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 43,9 Mb
Release : 2001-04-27
Category : Mathematics
ISBN : 0817638903

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State Spaces of Operator Algebras by Erik M. Alfsen,Frederik W. Shultz Pdf

The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.