Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A Panorama of Modern Operator Theory and Related TopicsBanach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group

A Panorama of Modern Operator Theory and Related Topics: Banach Algebras of Commuting Toeplitz... [We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in Cn. As was observed recently, apart of the already known commutative Toeplitz C * -algebras, quite unexpectedly, there exist many others, not geometrically defined, classes of symbols which generate commutative Toeplitz operator algebras on each weighted Bergman space. These classes of symbols were in a sense subordinated to the quasi-elliptic and quasi-parabolic groups of biholomorphisms of the unit ball. The corresponding commutative operator algebras were Banach, and being extended to the C * -algebras they became non-commutative. We consider here the case of symbols subordinated to the quasi-hyperbolic group and show that such classes of symbols are as well the sources for the commutative Banach algebras generated by Toeplitz operators. That is, together with the results of [11, 12], we cover the multidimensional extensions of all three model cases on the unit disk.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Panorama of Modern Operator Theory and Related TopicsBanach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group

Part of the Operator Theory: Advances and Applications Book Series (volume 218)
Editors: Dym, Harry; Kaashoek, Marinus A.; Lancaster, Peter; Langer, Heinz; Lerer, Leonid
Bauer, Wolfram; Vasilevski, Nikolai
Springer Journals — Jan 3, 2012
Download PDF
21 pages

Loading next page...
 
/lp/springer-journals/a-panorama-of-modern-operator-theory-and-related-topics-banach-ZLh8anehsa
Publisher
Springer Basel
Copyright
© Springer Basel AG 2012
ISBN
978-3-0348-0220-8
Pages
155 –175
DOI
10.1007/978-3-0348-0221-5_6
Publisher site
See Chapter on Publisher Site

Abstract

[We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in Cn. As was observed recently, apart of the already known commutative Toeplitz C * -algebras, quite unexpectedly, there exist many others, not geometrically defined, classes of symbols which generate commutative Toeplitz operator algebras on each weighted Bergman space. These classes of symbols were in a sense subordinated to the quasi-elliptic and quasi-parabolic groups of biholomorphisms of the unit ball. The corresponding commutative operator algebras were Banach, and being extended to the C * -algebras they became non-commutative. We consider here the case of symbols subordinated to the quasi-hyperbolic group and show that such classes of symbols are as well the sources for the commutative Banach algebras generated by Toeplitz operators. That is, together with the results of [11, 12], we cover the multidimensional extensions of all three model cases on the unit disk.]

Published: Jan 3, 2012

Keywords: Toeplitz operator; weighted Bergman space; unit ball; commutative Banach algebra; quasi-hyperbolic group

There are no references for this article.