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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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Isomorphism of the Toeplitz $C^ *$-algebras for the Hardy and Bergman spaces on certain Reinhardt domains
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by Albert Jeu-Liang Sheu PDF
Proc. Amer. Math. Soc. 116 (1992), 113-120 Request permission

Abstract:

I. Raeburn has conjectured that the Toeplitz ${C^*}$-algebras $\mathcal {T}(D)$ and $\mathcal {T}(\partial D)$ defined on the Bergman space ${H^2}(D)$ and the Hardy space ${H^2}(\partial D)$ of an arbitrary strongly pseudoconvex domain $D$ in ${\mathbb {C}^n}$ are isomorphic. Applying the groupoid ${C^*}$-algebra approach of Curto, Muhly, and Renault to ${C^*}$-algebras of Toeplitz type, we prove that this conjecture holds for (not even necessarily pseudoconvex) Reinhardt domains in ${\mathbb {C}^2}$ satisfying a mild boundary condition.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 113-120
  • MSC: Primary 47B35; Secondary 32A07, 46L05, 47D25
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1092926-9
  • MathSciNet review: 1092926