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An Operator Theory Problem Book

2018-10-15 Mathematics
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Release : 2018-10-15
Genre : Mathematics
Kind : eBook
Book Rating : 272/5 ( reviews)

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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. This book was released on 2018-10-15. 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.

Elements of Operator Theory

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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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. This book was released on 2013-03-14. 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.

A Hilbert Space Problem Book

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 302/5 ( reviews)

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Book Synopsis A Hilbert Space Problem Book by : P.R. Halmos

Download or read book A Hilbert Space Problem Book written by P.R. Halmos. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: "This book was written for the active reader. The first part consists of problems, frequently preceded by definitions and motivation, and sometimes followed by corollaries and historical remarks... The second part, a very short one, consists of hints... The third part, the longest, consists of solutions: proofs, answers, or contructions, depending on the nature of the problem.... This is not an introduction to Hilbert space theory. Some knowledge of that subject is a prerequisite: at the very least, a study of the elements of Hilbert space theory should proceed concurrently with the reading of this book."

Problems in Operator Theory

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 474/5 ( reviews)

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Book Synopsis Problems in Operator Theory by : Yuri A. Abramovich

Download or read book Problems in Operator Theory written by Yuri A. Abramovich. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This book contains complete solutions to the more than six hundred exercises in the authors' book: Invitation to operator theory--foreword.

Basic Operator Theory

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 851/5 ( reviews)

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Book Synopsis Basic Operator Theory by : Israel Gohberg

Download or read book Basic Operator Theory written by Israel Gohberg. This book was released on 2013-12-01. 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.

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