On Toeplitz operators on Bergman spaces of the unit polydisk
Author:
Trieu Le
Journal:
Proc. Amer. Math. Soc. 138 (2010), 275285
MSC (2000):
Primary 47B35
Published electronically:
August 25, 2009
MathSciNet review:
2550193
Fulltext PDF Free Access
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Abstract: We study Toeplitz operators on the Bergman space of the unit polydisk , where is a product of rotationinvariant 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 nonconstant bounded holomorphic function on , then what conditions does a bounded function need to satisfy so that commutes with ?
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 Guangfu Cao, On a problem of Axler, Cuckovic and Rao, Proc. Amer. Math. Soc. 136 (2008), no. 3, 931935 (electronic). MR 2361866 (2009a:47052)
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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:
http://dx.doi.org/10.1090/S0002993909100606
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.
