Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group

Wolfram Bauer; Nikolai Vasilevski

doi:10.1007/978-3-0348-0221-5_6

Details

Original language	English
Title of host publication	A Panorama of Modern Operator Theory and Related Topics
Subtitle of host publication	The Israel Gohberg Memorial Volume
Publisher	Springer Basel AG
Pages	155-175
Number of pages	21
ISBN (electronic)	9783034802215
ISBN (print)	9783034802208
Publication status	Published - 3 Jan 2012
Externally published	Yes

Publication series

Name	Operator Theory: Advances and Applications
Publisher	Springer Basel AG
Volume	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.

Keywords

Commutative Banach algebra, Quasi-hyperbolic group, Toeplitz operator, Unit ball, Weighted Bergman space

ASJC Scopus subject areas

Mathematics(all)
General Mathematics

Cite this

Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group. / Bauer, Wolfram; Vasilevski, Nikolai.
A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Springer Basel AG, 2012. p. 155-175 (Operator Theory: Advances and Applications; Vol. 218).

Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review

Bauer, W & Vasilevski, N 2012, Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group. in A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Operator Theory: Advances and Applications, vol. 218, Springer Basel AG, pp. 155-175. https://doi.org/10.1007/978-3-0348-0221-5_6

Bauer, W., & Vasilevski, N. (2012). Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group. In A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume (pp. 155-175). (Operator Theory: Advances and Applications; Vol. 218). Springer Basel AG. https://doi.org/10.1007/978-3-0348-0221-5_6

Bauer W, Vasilevski N. Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group. In A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Springer Basel AG. 2012. p. 155-175. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0348-0221-5_6

Bauer, Wolfram ; Vasilevski, Nikolai. / Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasi-hyperbolic Group. A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial Volume. Springer Basel AG, 2012. pp. 155-175 (Operator Theory: Advances and Applications).

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Research@Leibniz University