Commutative Algebras of Toeplitz Operators on the Bergman Space

Nikolai Vasilevski

ISBN 10: 3764387254 / ISBN 13: 9783764387259

Published by Birkhäuser Basel, Springer Basel Jul 2008, 2008

About this Item

Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 452 pp. Englisch.

Seller Inventory # 9783764387259

Bibliographic Details

• Title: Commutative Algebras of Toeplitz Operators on the Bergman Space
• Publisher: Birkhäuser Basel, Springer Basel Jul 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 3764387254
• ISBN 13: 9783764387259
• Binding: Buch
• Condition: Neu

About this title

Synopsis

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.

From the Back Cover

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.