On Toeplitz operators on Bergman spaces of the unit polydisk

Author:
Trieu Le

Journal:
Proc. Amer. Math. Soc. **138** (2010), 275-285

MSC (2000):
Primary 47B35

DOI:
https://doi.org/10.1090/S0002-9939-09-10060-6

Published electronically:
August 25, 2009

MathSciNet review:
2550193

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study Toeplitz operators on the Bergman space of the unit polydisk , where is a product of rotation-invariant regular Borel probability measures. We show that if is a bounded Borel function on such that exists for all , then is compact if and only if a.e. with respect to a measure associated with on the boundary . We also discuss the commuting problem: if is a non-constant bounded holomorphic function on , then what conditions does a bounded function need to satisfy so that commutes with ?

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Additional Information

**Trieu Le**

Affiliation:
Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1

Email:
t29le@math.uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9939-09-10060-6

Keywords:
Bergman space,
Toeplitz operator,
compact operator,
commuting problem

Received by editor(s):
November 9, 2008

Received by editor(s) in revised form:
May 28, 2009

Published electronically:
August 25, 2009

Communicated by:
Nigel J. Kalton

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.