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# ๐ Elements of Hilbert Spaces and Operator Theory by Harkrishan Lal Vasudeva โ free epub

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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.

## About book:

## About file:

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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:
**Harkrishan Lal Vasudeva** - Year:
**2017** - Publisher:
**Springer** - Language:
**English** - ISBN:

- File size:
**4 067 835** - Format:
**pdf**

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The subject of this book is operator theory on the Hardy space H[superscript 2], also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters t...

Real Analysis is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis. Here the focus is on the development of measure and integration theory, differen...

The authors develop elements of a general dilation theory for operator-valued measures. Hilbert space operator-valued measures are closely related to bounded linear maps on abelian von Neumann algebras, and some of their results include new dilation resul...

This volume contains contributions originating from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Newcastle upon Tyne in July 2004. The articles expertly cover a broad range of material at the cutting edge of functiona...

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, cons...

This textbook is an introduction to functional analysis suited to final year undergraduates or beginning graduates. Its various applications of Hilbert spaces, including least squares approximation, inverse problems, and Tikhonov regularization, should ap...

In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the pas...

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also dr...

The present lectures are based on a course deli vered by the authors at the Uni versi ty of Bucharest, in the winter semester 1985-1986. Without aiming at completeness, the topics selected cover all the major questions concerning hyponormal operators. Our...

This book provides a complete understanding of the jBPM technology stack. It starts with an introduction to the world of business process management systems, the problem domain addressed by jBPM, explores the main use cases that can be addressed by busine...