Numerical ranges of Hilbert space operators / Pei Yuan Wu, National Chiao Tung University, Taiwan, Hwa-Long Gau, National Central University, Taiwan.

Format:

Book

Author/Creator:

Wu, Pei Yuan, author.

Series:

Encyclopedia of mathematics and its applications ; 179.

Encyclopedia of mathematics and its applications ; 179

Language:

English

Subjects (All):

Hilbert space.

Operator theory.

Physical Description:

1 online resource (483 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.

Contents:

Cover

Half-title

Series information

Title page

Copyright information

Dedication

Contents

Preface

List of Symbols

Introduction: Preliminaries in Operator Theory

I.1 Basic Properties

I.2 Spectral Theory

I.3 Special Types of Operators

I.4 Matrix Theory

I.5 C[sup(*)]-Algebra Theory

I.6 Fredholm Theory

I.7 Compression and Dilation

1 Numerical Range

1.1 Basic Properties

1.2 Relation to Spectrum

1.3 Boundary and Interior

1.4 Limit and Transforms

1.5 Parameters

Problems

2 Numerical Ranges of Special Operators

2.1 Quadratic Operator

2.2 Normal Operator

2.3 Hyponormal and Toeplitz Operators

2.4 Weighted Shift

2.5 Composition Operator

2.6 Attainment Problem

3 Numerical Contraction

3.1 Numerical Radius

3.2 Numerical Contraction

3.3 Power Inequality and Ando's Theorem

3.4 Commuting Product

4 Algebraic and Essential Numerical Ranges

4.1 Algebraic Numerical Range

4.2 Essential Numerical Range

4.3 Commutator and Zero-Diagonal Operator

4.4 Total Dilation

4.5 Compact Operator

5 Numerical Range and Dilation

5.1 Unitary Dilation

5.2 Berger Power Dilation

5.3 Nilpotent Dilation

5.4 Spectral Set

6 Numerical Range of Finite Matrix

6.1 Kippenhahn Curve

6.2 3-by-3 Matrix

6.3 Anderson's Theorem

6.4 Line Segment

6.5 Nonnegative Matrix

7 Numerical Range of S[sub(n)]-Matrix

7.1 Basic Properties

7.2 Poncelet's Porism

7.3 Generalized Brianchon-Ceva and Lucas-Siebeck Theorems

7.4 Extension to Inflation of S([phi])

7.5 Norms of Powers and Gau-Wu Number

8 Generalized Numerical Ranges

8.1 Joint Numerical Range

8.2 C-Numerical Range

8.3 q-Numerical Range and Davis-Wielandt Shell

8.4 Matricial Ranges.

8.5 Higher-Rank Numerical Range

8.6 Zero-Dilation Index

Appendix Convex Set

A.1 Basic Properties

A.2 Boundary Parametrization

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 27 Jul 2021).

ISBN:

1-108-78760-6

1-108-80641-4

1-108-78229-9

OCLC:

1262691566