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

Sheu, Albert Jeu-Liang

doi:10.1090/S0002-9939-1992-1092926-9

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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