Analytic Theory Of Subnormal Operators

Analytic Theory Of Subnormal Operators

by Daoxing Xia

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Overview

Analytic Theory Of Subnormal Operators by Daoxing Xia

This volume contains an important progress on the theory of subnormal operators in the past thirty years, which was developed by the author and his collaborators. It serves as a guide and basis to students and researchers on understanding and exploring further this new direction in operator theory. The volume expounds lucidly on analytic model theory, mosaics, trace formulas of the subnormal operators, and subnormal tuples of operators on the Hilbert spaces.

Product Details

ISBN-13: 9789814641333
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 12/30/2014
Pages: 228
Product dimensions: 6.68(w) x 9.10(h) x 0.71(d)

Table of Contents

Preface vii

1 Subnormal Operators 1

1.1 Subnormal operators 1

1.2 Block-matrix decomposition of a pure operator 3

1.3 Analytic model for a subnormal operator 9

1.4 Mosaic 20

1.5 Dual operator and some kind of spectra of pure subnormal operators 32

1.6 Subnormal operators with compact self-commutator 42

1.7 Complete unitary invariant for some subnormal operators 47

2 Subnormal Operators with Finite Rank Self-Commutators 55

2.1 Operator with rank one self-commutator 55

2.2 Decomposition of the mosaic 58

2.3 The reproducing kernel Hilbert space model 68

2.4 Area integral formula and trace formula 71

3 Analytic Model for Subnormal k-Tuple of Operators 77

3.1 Subnormal k-tuple of operators 77

3.2 Block-matrix decomposition of a pure k-tuple of commuting operators 81

3.3 Some operator identities 88

3.4 Analytic model for a subnormal k-tuple of operators 100

3.5 Mosaic 112

3.6 Operator identities for the products of resolvents and mosaic 120

3.7 Subnormal tuple of operators with compact self-commutators 128

4 Subnormal Tuple of Operators with Finite Dimension Defect Space 133

4.1 Spectrum of the minimal normal extension 133

4.2 Joint point spectrum and joint eigenvectors 138

4.3 Domains in some analytic manifold 142

4.4 Trace formulas 147

5 Etyponormal Operators with Finite Rank Self-Commutators 151

5.1 Hyponormal operators with rank one self-commutator 151

5.2 Analytic model of hyponormal operator with rank one self-commutator 154

5.3 Hyponormal operator associated with a quadrature domain 159

5.4 Mosaic for hyponormal operator associated with a quadrature domain 165

5.5 The inner product on an invariant subspaee 170

5.6 Simply connected quadrature domains 176

5.7 Operator of finite type 184

5.8 The reproducing kernels for operators of finite type 189

5.9 Trace formulas for some operators of finite type 194

Appendix A The Singular Integral Model, Mosaic and Trace Formula of Hyponormal Operator 199

Appendix B Quadrature Domain 201

Bibliography 203

Index 215

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