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Isomorphism of the Toeplitz $ C\sp *$-algebras for the Hardy and Bergman spaces on certain Reinhardt domains

Author: Albert Jeu-Liang Sheu
Journal: Proc. Amer. Math. Soc. 116 (1992), 113-120
MSC: Primary 47B35; Secondary 32A07, 46L05, 47D25
MathSciNet review: 1092926
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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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