Read While You Wait - Get immediate ebook access, if available*, when you order a print book

Operator Theory: Advances and Applications

Commutative Algebras of Toeplitz Operators on the Bergman Space

Authors: Vasilevski, Nikolai

Free Preview
  • First and unique book in which commutative C*-algebras of Toeplitz operators are considered
  • Starting from an introduction, 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
see more benefits

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-7643-8726-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-7643-8725-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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.

 

 

Reviews

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)

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $129.00
price for USA in USD
  • ISBN 978-3-7643-8726-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.99
price for USA in USD
  • ISBN 978-3-7643-8725-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Commutative Algebras of Toeplitz Operators on the Bergman Space
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
185
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8726-6
DOI
10.1007/978-3-7643-8726-6
Hardcover ISBN
978-3-7643-8725-9
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XXIX, 418
Topics

*immediately available upon purchase as print book shipments may be delayed due to the COVID-19 crisis. ebook access is temporary and does not include ownership of the ebook. Only valid for books with an ebook version. Springer Reference Works and instructor copies are not included.