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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Berezin transform and radial operators
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by Nina Zorboska PDF
Proc. Amer. Math. Soc. 131 (2003), 793-800 Request permission

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 $L^{1}(\mathbb {D})$ symbol.
References
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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
  • Received by editor(s): February 6, 2001
  • Received by editor(s) in revised form: October 12, 2001
  • Published electronically: July 2, 2002
  • Additional Notes: This work was supported by an NSERC grant
  • Communicated by: David R. Larson
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 793-800
  • MSC (2000): Primary 47B37, 47B10; Secondary 47B35
  • DOI: https://doi.org/10.1090/S0002-9939-02-06691-1
  • MathSciNet review: 1937440