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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Toeplitz and Hankel operators on Bergman spaces


Authors: Karel Stroethoff and De Chao Zheng
Journal: Trans. Amer. Math. Soc. 329 (1992), 773-794
MSC: Primary 47B35; Secondary 32A35, 46E20
MathSciNet review: 1112549
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Abstract: In this paper we consider Toeplitz and Hankel operators on the Bergman spaces of the unit ball and the polydisk in $ {\mathbb{C}^n}$ whose symbols are bounded measurable functions. We give necessary and sufficient conditions on the symbols for these operators to be compact. We study the Fredholm theory of Toeplitz operators for which the corresponding Hankel operator is compact. For these Toeplitz operators the essential spectrum is computed and shown to be connected. We also consider symbols that extend to continuous functions on the maximal ideal space of $ {H^\infty }(\Omega )$; for these symbols we describe when the Toeplitz or Hankel operators are compact.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1112549-7
PII: S 0002-9947(1992)1112549-7
Article copyright: © Copyright 1992 American Mathematical Society