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The Berezin transform and radial operators
Author(s):
Nina
Zorboska
Journal:
Proc. Amer. Math. Soc.
131
(2003),
793-800.
MSC (2000):
Primary 47B37, 47B10;
Secondary 47B35
Posted:
July 2, 2002
MathSciNet review:
1937440
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Abstract:
We analyze the connection between compactness of operators on the Bergman space and the boundary behaviour of the corresponding Berezin transform. We prove that for a special class of operators that we call radial operators, an oscilation criterion is a sufficient condition under which the compactness of an operator is equivalent to the vanishing of the Berezin transform on the unit circle. We further study a special class of radial operators, i.e., Toeplitz operators with a radial  symbol.
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Additional Information:
Nina
Zorboska
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email:
zorbosk@cc.umanitoba.ca
DOI:
10.1090/S0002-9939-02-06691-1
PII:
S 0002-9939(02)06691-1
Keywords:
Berezin transform,
radial operator,
Toeplitz operator
Received by editor(s):
February 6, 2001
Received by editor(s) in revised form:
October 12, 2001
Posted:
July 2, 2002
Additional Notes:
This work was supported by an NSERC grant
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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