Structure of Hilbert space operators / Chunlan Jiang, Zongyao Wang.

Format:

Book

Author/Creator:

Jiang, Chunlan.

Contributor:

Wang, Zongyao.

Class of 1932 Fund.

Language:

English

Subjects (All):

Hilbert space.

Linear operators.

Physical Description:

x, 248 pages ; 24 cm

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, 2006.

Summary:

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. Book jacket.

Contents:

1.1 Banach Algebra 1

1.2 K-Theory of Banach Algebra 3

1.3 The Basic of Complex Geometry 4

1.4 Some Results on Cowen-Douglas Operators 5

1.5 Strongly Irreducible Operators 7

1.6 Compact Perturbation of Operators 9

1.7 Similarity Orbit Theorem 9

1.8 Toeplitz Operator and Sobolev Space 10

2 Jordan Standard Theorem and K[subscript 0]-Group 13

2.1 Generalized Eigenspace and Minimal Idempotents 13

2.2 Similarity Invariant of Matrix 14

3 Approximate Jordan Theorem of Operators 19

3.1 Sum of Strongly Irreducible Operators 19

3.2 Approximate Jordan Decomposition Theorem 29

4 Unitary Invariant and Similarity Invariant of Operators 43

4.1 Unitary Invariants of Operators 44

4.2 Strongly Irreducible Decomposition of Operators and Similarity Invariant: K[subscript 0]-Group 57

4.3 (SI) Decompositions of Some Classes of Operators 69

4.4 The Commutant of Cowen-Douglas Operators 80

4.5 The Sobolev Disk Algebra 94

4.6 The Operator Weighted Shift 126

5 The Similarity Invariant of Cowen-Douglas Operators 149

5.1 The Cowen-Douglas Operators with Index 1 149

5.2 Cowen-Douglas Operators with Index n 154

5.3 The Commutant of Cowen-Douglas Operators 157

5.4 The Commutant of a Classes of Operators 169

5.5 The (SI) Representation Theorem of Cowen-Douglas Operators 176

5.6 Maximal Ideals of The Commutant of Cowen-Douglas Operators 189

5.7 Some Approximation Theorem 192

6 Some Other Results About Operator Structure 203

6.1 K[subscript 0]-Group of Some Banach Algebra 203

6.2 Similarity and Quasisimilarity 206

6.3 Application of Operator Structure Theorem 237.

Notes:

Includes bibliographical references (pages 241-246) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1932 Fund.

ISBN:

9812566163

OCLC:

70141862