Basic Operator Theory

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Basic Operator Theory

Author : Israel Gohberg
Publisher : Birkhäuser
ISBN 13 : 1461259851
Total Pages : 291 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Basic Operator Theory by : Israel Gohberg

Download or read book Basic Operator Theory written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-12-01 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic Operator Theory

Author : Israel Gohberg
Publisher : Birkhäuser
ISBN 13 : 0817642625
Total Pages : 304 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Basic Operator Theory by : Israel Gohberg

Download or read book Basic Operator Theory written by Israel Gohberg and published by Birkhäuser. This book was released on 2001-08-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elements of Operator Theory

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
ISBN 13 : 1475733283
Total Pages : 535 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Elements of Operator Theory by : Carlos S. Kubrusly

Download or read book Elements of Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: {\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.

Basic Operator Theory

Author : Israel Gohberg
Publisher :
ISBN 13 : 9781461259862
Total Pages : 304 pages
Book Rating : 4.2/5 (598 download)

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Book Synopsis Basic Operator Theory by : Israel Gohberg

Download or read book Basic Operator Theory written by Israel Gohberg and published by . This book was released on 2014-09-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Basic Operator Theory

Author : Yiśrāʿēl Z. Gohberg
Publisher :
ISBN 13 : 9783764342623
Total Pages : 285 pages
Book Rating : 4.3/5 (426 download)

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Book Synopsis Basic Operator Theory by : Yiśrāʿēl Z. Gohberg

Download or read book Basic Operator Theory written by Yiśrāʿēl Z. Gohberg and published by . This book was released on 2001 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elements of Hilbert Spaces and Operator Theory

Author : Harkrishan Lal Vasudeva
Publisher : Springer
ISBN 13 : 9811030200
Total Pages : 528 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Elements of Hilbert Spaces and Operator Theory by : Harkrishan Lal Vasudeva

Download or read book Elements of Hilbert Spaces and Operator Theory written by Harkrishan Lal Vasudeva and published by Springer. This book was released on 2017-03-27 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic Classes of Linear Operators

Author : Israel Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034879806
Total Pages : 428 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg

Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in Operator Theory

Author : John B. Conway
Publisher : American Mathematical Soc.
ISBN 13 : 0821820656
Total Pages : 390 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Course in Operator Theory by : John B. Conway

Download or read book A Course in Operator Theory written by John B. Conway and published by American Mathematical Soc.. This book was released on 2000 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

C*-Algebras and Operator Theory

Author : Gerald J. Murphy
Publisher : Academic Press
ISBN 13 : 0080924964
Total Pages : 297 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis C*-Algebras and Operator Theory by : Gerald J. Murphy

Download or read book C*-Algebras and Operator Theory written by Gerald J. Murphy and published by Academic Press. This book was released on 2014-06-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operator Theory

Author : Daniel Alpay
Publisher : Springer
ISBN 13 : 9783034806664
Total Pages : 0 pages
Book Rating : 4.8/5 (66 download)

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Book Synopsis Operator Theory by : Daniel Alpay

Download or read book Operator Theory written by Daniel Alpay and published by Springer. This book was released on 2015-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-sentence definition of operator theory could be: The study of (linear) continuous operations between topological vector spaces, these being in general (but not exclusively) Fréchet, Banach, or Hilbert spaces (or their duals). Operator theory is thus a very wide field, with numerous facets, both applied and theoretical. There are deep connections with complex analysis, functional analysis, mathematical physics, and electrical engineering, to name a few. Fascinating new applications and directions regularly appear, such as operator spaces, free probability, and applications to Clifford analysis. In our choice of the sections, we tried to reflect this diversity. This is a dynamic ongoing project, and more sections are planned, to complete the picture. We hope you enjoy the reading, and profit from this endeavor.

Operator Theory for Electromagnetics

Author : George W. Hanson
Publisher : Springer Science & Business Media
ISBN 13 : 1475736797
Total Pages : 640 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Operator Theory for Electromagnetics by : George W. Hanson

Download or read book Operator Theory for Electromagnetics written by George W. Hanson and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Unbounded Linear Operators

Author : Seymour Goldberg
Publisher : Courier Corporation
ISBN 13 : 0486453316
Total Pages : 212 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Unbounded Linear Operators by : Seymour Goldberg

Download or read book Unbounded Linear Operators written by Seymour Goldberg and published by Courier Corporation. This book was released on 2006-01-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory. After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations. In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols.

An Operator Theory Problem Book

Author : Mohammed Hichem Mortad
Publisher : World Scientific
ISBN 13 : 9813236272
Total Pages : 656 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis An Operator Theory Problem Book by : Mohammed Hichem Mortad

Download or read book An Operator Theory Problem Book written by Mohammed Hichem Mortad and published by World Scientific. This book was released on 2018-10-15 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory of Linear Operators

Author : Vladimir Müller
Publisher : Springer Science & Business Media
ISBN 13 : 3764382651
Total Pages : 444 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Spectral Theory of Linear Operators by : Vladimir Müller

Download or read book Spectral Theory of Linear Operators written by Vladimir Müller and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Operators on Hilbert Space

Author : V. S. Sunder
Publisher : Springer
ISBN 13 : 9811018162
Total Pages : 107 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Operators on Hilbert Space by : V. S. Sunder

Download or read book Operators on Hilbert Space written by V. S. Sunder and published by Springer. This book was released on 2016-08-05 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primarily objective of the book is to serve as a primer on the theory of bounded linear operators on separable Hilbert space. The book presents the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus. It discusses a proof without digressing into a course on the Gelfand theory of commutative Banach algebras. The book also introduces the reader to the basic facts concerning the various von Neumann–Schatten ideals, the compact operators, the trace-class operators and all bounded operators.

An Introduction to Models and Decompositions in Operator Theory

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
ISBN 13 : 1461219981
Total Pages : 141 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis An Introduction to Models and Decompositions in Operator Theory by : Carlos S. Kubrusly

Download or read book An Introduction to Models and Decompositions in Operator Theory written by Carlos S. Kubrusly and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a Hilbert-space operator we mean a bounded linear transformation be tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.

Classes of Linear Operators

Author : Israel Gohberg
Publisher : Birkhauser
ISBN 13 :
Total Pages : 494 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Classes of Linear Operators by : Israel Gohberg

Download or read book Classes of Linear Operators written by Israel Gohberg and published by Birkhauser. This book was released on 1990 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: