Commutative Algebras of Toeplitz Operators on the Bergman Space

• Main Author: Vasilevski, Nikolai L. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Operator Theory: Advances and Applications ; 185
• Subjects: Mathematics.; Functional analysis.; Functions of complex variables.; Operator theory.; Operator Theory.; Functions of a Complex Variable.; Functional Analysis.

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...

Table of 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.