Toeplitz and Hankel operators on Bergman spaces
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- by Karel Stroethoff and De Chao Zheng PDF
- Trans. Amer. Math. Soc. 329 (1992), 773-794 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 773-794
- MSC: Primary 47B35; Secondary 32A35, 46E20
- DOI: https://doi.org/10.1090/S0002-9947-1992-1112549-7
- MathSciNet review: 1112549