Structure Of Hilbert Space Operators

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Structure Of Hilbert Space Operators

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Author : Chunlan Jiang
language : en
Publisher: World Scientific
Release Date : 2006-03-01

Structure Of Hilbert Space Operators written by Chunlan Jiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-01 with Mathematics categories.

This book exposes the internal structure of non-self-adjoint operators acting on complex separable infinite dimensional Hilbert space, by analyzing and studying the commutant of operators. A unique presentation of the theorem of Cowen-Douglas operators is given. The authors take the strongly irreducible operator as a basic model, and find complete similarity invariants of Cowen-Douglas operators by using K-theory, complex geometry and operator algebra tools.

Structure Theorems For Certain Semi Groups Of Hilbert Space Operators

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Author : Fred Douglas Beers
language : en
Publisher:
Release Date : 1974

Structure Theorems For Certain Semi Groups Of Hilbert Space Operators written by Fred Douglas Beers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Hilbert space categories.

Hilbert Space Operators

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Author : Carlos S. Kubrusly
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Hilbert Space Operators written by Carlos S. Kubrusly and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that range from the straightforward to the state-of-the-art. Complete solutions to all problems are provided. The text covers the basics of bounded linear operators on a Hilbert space and gradually progresses to more advanced topics in spectral theory and quasireducible operators. Written in a motivating and rigorous style, the work has few prerequisites beyond elementary functional analysis, and will appeal to graduate students and researchers in mathematics, physics, engineering, and related disciplines.

Elements Of Hilbert Spaces And Operator Theory

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Author : Harkrishan Lal Vasudeva
language : en
Publisher: Springer
Release Date : 2017-03-27

Elements Of Hilbert Spaces And Operator Theory written by Harkrishan Lal Vasudeva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-27 with Mathematics categories.

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.

A Structure Theory For Some Nearly Normal Hilbert Space Operators

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Author : James Wallace Del Valle
language : en
Publisher:
Release Date : 1974

A Structure Theory For Some Nearly Normal Hilbert Space Operators written by James Wallace Del Valle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Characteristic functions categories.

A Primer On Hilbert Space Operators

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Author : Piotr Sołtan
language : en
Publisher: Springer
Release Date : 2018-09-04

A Primer On Hilbert Space Operators written by Piotr Sołtan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-04 with Mathematics categories.

The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.

Strongly Irreducible Operators On Hilbert Space

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Author : ChunLan Jiang
language : en
Publisher: Taylor & Francis
Release Date : 2023-02-15

Strongly Irreducible Operators On Hilbert Space written by ChunLan Jiang and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-15 with Mathematics categories.

This volume provides a comprehensive treatment of strongly irreducible operators acting on a complex separable infinite dimensional Hilbert space, and to expose and reflect the internal structure of operators by analyzing and studying irreducibility of operators. Much of the material presented here appears in book form for the first time.

Hilbert Space Operators

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Author : J.M. Bachar
language : en
Publisher: Springer
Release Date : 2006-11-15

Hilbert Space Operators written by J.M. Bachar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Harmonic Analysis Of Operators On Hilbert Space

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Author : Béla Sz Nagy
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-01

Harmonic Analysis Of Operators On Hilbert Space written by Béla Sz Nagy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-01 with Mathematics categories.

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.

An Introduction To Operators On The Hardy Hilbert Space

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Author : Ruben A. Martinez-Avendano
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-12

An Introduction To Operators On The Hardy Hilbert Space written by Ruben A. Martinez-Avendano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-12 with Mathematics categories.

This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.