Title: Reinhardt domains, boundary geometry, and Toeplitz C∗-algebras
Abstract: In this paper, we have found explicitly how the boundary geometry of a Reinhardt domain in C2 determines the structure of its Toeplitz C∗-algebra. More precisely, our main result is an explicit simple algorithm to describe the structure of the Toeplitz C∗-algebra of a Reinhardt domain D in C2 (satisfying some mild boundary condition) in terms of rotation C∗-algebras, based on the degree of contact of the boundary curve of C, the logarithmic domain of D at each point of intersection with the linear faces of the convex hull of C, and the slopes of these faces. A consequence of this result is that the Toeplitz C∗-algebras T(D) and T(D̃) of D and its pseudoconvex hull D̃ are rarely isomorphic, but are always of the same type (i.e., either both are of type I or both are not of type I). In other words, the isomorphism class of T(D) is usually changed under taking pseudoconvex hull but the type of T(D) is not affected.
Publication Year: 1990
Publication Date: 1990-08-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 6
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