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\(K\)-groups of Toeplitz algebras of Reinhardt domains. (English) Zbl 0898.46061

The Toeplitz \(C^*\)-algebra \({\mathcal T}(D)\) of a Reinhardt domain \(D\) in \(\mathbb{C}^2\) is investigation. The author shows that under some restrictions on the boundary of \(D\), \({\mathcal T}(D)\) contains Fredholm operators of any given indices and he computes the \(K\)-groups of \({\mathcal T}(D)\). He gets that these \(K\)-groups are free Abelian with ranks determined by the boundary geometry of \(D\).

MSC:

46L80 \(K\)-theory and operator algebras (including cyclic theory)
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46L05 General theory of \(C^*\)-algebras
47A53 (Semi-) Fredholm operators; index theories
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