Commutative Algebras of Toeplitz Operators on the Bergman Space

• 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.

From the reviews: "This is a massive, detailed, and comprehensive book on the theory of Toeplitz operators and Toeplitz algebras ... . The book is quite easy to read and understand. Computations as well are explicit and detailed. ... Included Highlights of the chapters in addition to Preface and Introduction will be helpful for the readers to decide and read this book properly and effectively. Furthermore, Bibliographical Remarks for items in the Bibliography will also be helpful for further reading." (Takahiro Sudo, Zentralblatt MATH, Vol. 1168, 2009)