Sheu, Albert Jeu-Liang \(K\)-groups of Toeplitz algebras of Reinhardt domains. (English) Zbl 0898.46061 Math. Scand. 75, No. 2, 280-292 (1994). 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 \(D\). Reviewer: K.Georgiev (Rostov-na-Donu) Cited in 1 Document 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 Keywords:Toeplitz \(C^*\)-algebra; Reinhardt domain; Fredholm operators; \(K\)-groups; boundary geometry PDFBibTeX XMLCite \textit{A. J. L. Sheu}, Math. Scand. 75, No. 2, 280--292 (1994; Zbl 0898.46061) Full Text: DOI EuDML