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

Format:

Book

Author/Creator:

Jiang, Chunlan.

Contributor:

Wang, Zongyao.

Language:

English

Subjects (All):

Hilbert space.

Linear operators.

Physical Description:

1 online resource (x, 248 p.)

Edition:

1st ed.

Place of Publication:

Hackensack, NJ : World Scientific, 2006.

Language Note:

English

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.

Contents:

Preface

1. Background. 1.1. Banach algebra. 1.2. K-theory of Banach algebra. 1.3. The basic of complex geometry. 1.4. Some results on Cowen-Douglas operators. 1.5. Strongly irreducible operators. 1.6. Compact perturbation of operators. 1.7. Similarity orbit theorem. 1.8. Toeplitz operator and Sobolev space

2. Jordan standard theorem and K[symbol]-group. 2.1. Generalized Eigenspace and minimal idempotents. 2.2. Similarity invariant of matrix. 2.3. Remark

3. Approximate Jordan theorem of operators. 3.1. Sum of strongly irreducible operators. 3.2. Approximate Jordan decomposition theorem. 3.3. Open problems. 3.4. Remark

4. Unitary invariant and similarity invariant of operators. 4.1. Unitary invariants of operators. 4.2. Strongly irreducible decomposition of operators and similarity invariant: K[symbol]-group. 4.3. (SI) decompositions of some classes of operators. 4.4. The commutant of Cowen-Douglas operators. 4.5. The Sobolev disk algebra. 4.6. The operator weighted shift. 4.7. Open problem. 4.8. Remark

5. The similarity invariant of Cowen-Douglas operators. 5.1. The Cowen-Douglas operators with index 1. 5.2. Cowen-Douglas operators with index n. 5.3. The commutant of Cowen-Douglas operators. 5.4. The commutant of a classes of operators. 5.5. The (5I) representation theorem of Cowen-Douglas operators. 5.6. Maximal ideals of the commutant of Cowen-Douglas operators. 5.7. Some approximation theorem. 5.8. Remark. 5.9. Open problem

6. Some other results about operator structure. 6.1. K[symbol]-group of some Banach algebra. 6.2. Similarity and quasisimilarity. 6.3. Application of operator structure theorem. 6.4. Remark. 6.5. Open problems.

Notes:

Bibliographic Level Mode of Issuance: Monograph

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

ISBN:

9786611919511

9781281919519

1281919519

9789812774484

9812774483

OCLC:

879025635