Commutative algebras of Toeplitz operators on the Bergman space / Nikolai L. Vasilevski.

Format:

Book

Author/Creator:

Vasilevski, Nikolai.

Series:

Operator theory, advances and applications ; v. 185.

Operator theory, advances and applications ; v. 185

Language:

English

Subjects (All):

Bergman spaces.

Commutative algebra.

Toeplitz operators.

Physical Description:

1 online resource (443 p.)

Edition:

1st ed. 2008.

Place of Publication:

Basel : Birkhauser ; [London : Springer, distributor], 2008.

Language Note:

English

Summary:

This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitz operators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitz operators studied herein, such as boundedness, compactness, spectral properties, invariant subspaces. The presence and exploitation of these spectral type representations forms the core for many results presented in the book. Among other results it contains a criterion of when the algebras are commutative on each commonly considered weighted Bergman space together with their explicit descriptions; a systematic study of Toeplitz operators with unbounded symbols; a clarification of the difference between compactness of commutators and semi-commutators of Toeplitz operators; the theory of Toeplitz and related operators with symbols having more than two limit values at boundary points; and a kind of semi-classical analysis of spectral properties of Toeplitz operators. The book is addressed to a wide audience of mathematicians, from graduate students to researchers, whose primary interests lie in complex analysis and operator theory. .

Contents:

Preliminaries

Prologue

Bergman and Poly-Bergman Spaces

Bergman Type Spaces on the Unit Disk

Toeplitz Operators with Commutative Symbol Algebras

Toeplitz Operators on the Unit Disk with Radial Symbols

Toeplitz Operators on the Upper Half-Plane with Homogeneous Symbols

Anatomy of the Algebra Generated by Toeplitz Operators with Piece-wise continuous Symbols

Commuting Toeplitz Operators and Hyperbolic Geometry

Weighted Bergman Spaces

Commutative Algebras of Toeplitz Operators

Dynamics of Properties of Toeplitz Operators with Radial Symbols

Dynamics of Properties of Toeplitz Operators on the Upper Half-Plane: Parabolic Case

Dynamics of Properties of Toeplitz Operators on the Upper Half-Plane: Hyperbolic Case.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9783764387266

3764387262

OCLC:

304518938