Elements of Hilbert spaces and operator theory / Harkrishan Lal Vasudeva ; with contributions from Satish Shirali.
2017
QA322.4
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Title
Elements of Hilbert spaces and operator theory / Harkrishan Lal Vasudeva ; with contributions from Satish Shirali.
ISBN
9789811030208 (electronic book)
9811030200 (electronic book)
9789811030192
9811030197
9811030200 (electronic book)
9789811030192
9811030197
Published
Singapore : Springer, 2017.
Language
English
Description
1 online resource (xiii, 522 pages) : illustrations
Item Number
10.1007/978-981-10-3020-8 doi
Call Number
QA322.4
Dewey Decimal Classification
515/.733
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed April 7, 2017).
Available in Other Form
Print version: 9789811030192
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Table of Contents
Preface
Preliminaries
Inner Product Spaces
Linear Operators
Spectral Theory and Special Classes of Operators
Banach Spaces
Hints and Solutions
References
Index. .
Preliminaries
Inner Product Spaces
Linear Operators
Spectral Theory and Special Classes of Operators
Banach Spaces
Hints and Solutions
References
Index. .