Operator theory: advances and applications : commutative algebras of Toeplitz operators on the Bergman space

This 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.The key point to understand their structure and classify them surprisingly lies in the hyperbolic geometry of the unit disk. We develop as well a number ofimportant problems whose successful solution was made possible and is based on the specific features of the Toeplitz operators from these commutative algebras. 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 INDICE: 1. Prologue. 2. Bergman and Poly-Bergman Spaces. 3. Bergman-Type Spaces on the Unit Disk. 4. Toeplitz Operators with Commutative Symbol Algebras. 5. Toeplitz Operators on the Unit Disk with Radial Symbols. 6. Toeplitz Operators with Homogeneous Symbols. 7. Anatomy of the Algebra Generated by Toeplitz Operators. 8. Toeplitz Operators and Hyperbolic Geometry. 9. Weighted Bergman spaces. 10. Commutative Algebras of Toeplitz Operators. 11. Dynamics of Properties, Radial Symbols. 12. Dynamics of Properties, Parabolic case. 13. Dynamics of Properties, Hyperbolic case. Appendices. References. Index.

• ISBN: 978-3-7643-8725-9
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 400
• Fecha Publicación: 01/06/2008
• Nº Volúmenes: 1
• Idioma: Inglés