Details
| Originalsprache | Englisch |
|---|---|
| Titel des Sammelwerks | A Panorama of Modern Operator Theory and Related Topics |
| Untertitel | The Israel Gohberg Memorial Volume |
| Herausgeber (Verlag) | Springer Basel AG |
| Seiten | 155-175 |
| Seitenumfang | 21 |
| ISBN (elektronisch) | 9783034802215 |
| ISBN (Print) | 9783034802208 |
| Publikationsstatus | Veröffentlicht - 3 Jan. 2012 |
| Extern publiziert | Ja |
Publikationsreihe
| Name | Operator Theory: Advances and Applications |
|---|---|
| Herausgeber (Verlag) | Springer Basel AG |
| Band | 218 |
Abstract
We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in ℂ. 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Springer Basel AG, 2012. S. 155-175 (Operator Theory: Advances and Applications; Band 218).
Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Beitrag in Buch/Sammelwerk › Forschung › Peer-Review
}
TY - CHAP
T1 - Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group
AU - Bauer, Wolfram
AU - Vasilevski, Nikolai
N1 - Publisher Copyright: © 2012 Springer Basel AG. All rights reserved. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2012/1/3
Y1 - 2012/1/3
N2 - We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in ℂ. 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.
AB - We continue the study of commutative algebras generated by Toeplitz operators acting on the weighted Bergman spaces over the unit ball Bn in ℂ. 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.
KW - Commutative Banach algebra
KW - Quasi-hyperbolic group
KW - Toeplitz operator
KW - Unit ball
KW - Weighted Bergman space
UR - http://www.scopus.com/inward/record.url?scp=85013935952&partnerID=8YFLogxK
U2 - 10.1007/978-3-0348-0221-5_6
DO - 10.1007/978-3-0348-0221-5_6
M3 - Contribution to book/anthology
AN - SCOPUS:85013935952
SN - 9783034802208
T3 - Operator Theory: Advances and Applications
SP - 155
EP - 175
BT - A Panorama of Modern Operator Theory and Related Topics
PB - Springer Basel AG
ER -