Overview
- First and unique book in which commutative C*-algebras of Toeplitz operators are considered
- Starting from an introduction to the area the book leads readers to new, up-to-date results on the currently very active area of modern operator theory
- Presents new tools in the theory of Toeplitz operators based on the unique features of Toeplitz operators which generate commutative algebras
- Includes supplementary material: sn.pub/extras
Part of the book series: Operator Theory: Advances and Applications (OT, volume 185)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Commutative Algebras of Toeplitz Operators on the Bergman Space
Authors: Nikolai L. Vasilevski
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-7643-8726-6
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2008
Hardcover ISBN: 978-3-7643-8725-9Published: 17 July 2008
eBook ISBN: 978-3-7643-8726-6Published: 20 November 2008
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XXIX, 418
Topics: Operator Theory, Functions of a Complex Variable, Functional Analysis