Commutative Algebras of Toeplitz Operators on the Bergman Space
Published on 17. July 2008
Book
Hardback
XXIX, 418 pages
978-3-7643-8725-9 (ISBN)
Description
This unique book is devoted to the detailed study of the recently discovered commutative C*-algebras of Toeplitz operators on the Bergman space over the unit disk. Surprisingly, the key point to understanding their structure and classifying them lies in the hyperbolic geometry of the unit disk. The book develops a number of important problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras.
Reviews / Votes
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)More details
Series
Edition
2008 ed.
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XXIX, 418 p.
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 30 mm
Weight
956 gr
ISBN-13
978-3-7643-8725-9 (9783764387259)
DOI
10.1007/978-3-7643-8726-6
Schweitzer Classification
Other editions
Additional editions
Nikolai Vasilevski
Commutative Algebras of Toeplitz Operators on the Bergman Space
E-Book
11/2008
1st Edition
Birkhäuser
€96.29
Available for download
Person
Nikolai Vasilevski was a professor at the Department of Mathematics of CINVESTAV del I.P.N., Mexico City, Mexico. He moved there in 1992 from Odessa, Ukraine, where he worked at the Department of Mathematics of Odessa State University.
He is the author of the monograph "Commutative Algebras of Toeplitz Operators on the Bergman Space" appeared at Birkhäuser in 2008.
Content
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.