Berezin-Toeplitz quantization and composition formulas

authored by

Wolfram Bauer

Abstract

Extending results in [L.A. Coburn, The measure algebra of the Heisenberg group, J. Funct. Anal. 161 (1999) 509-525; L.A. Coburn, On the Berezin-Toeplitz calculus, Proc. Amer. Math. Soc. 129 (11) (2001) 3331-3338] we derive composition formulas for Berezin-Toeplitz operators with i.g. unbounded symbols in the range of certain integral transforms. The question whether a finite product of Berezin-Toeplitz operators is an operator of this type again can be answered affirmatively in several cases, but there are also well-known counter examples. We explain some consequences of such formulas to C^*-algebras generated by Toeplitz operators.

External Organisation(s)

University of Greifswald

Type

Article

Journal

Journal of functional analysis

Volume

256

Pages

3107-3142

No. of pages

36

ISSN

0022-1236

Publication date

18.03.2009

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Analysis

Electronic version(s)

https://doi.org/10.1016/j.jfa.2008.10.002 (Access: Closed)