K-theory of Toeplitz \(C^*\)-algebras on Lie spheres
type: Item
instance of: scholarly article
title: K-theory of Toeplitz \(C^*\)-algebras on Lie spheres
zbMATH Open document ID: 0731.46037
DOI: 10.1007/BF01194930
author: Matthias Lesch
published in: Integral Equations and Operator Theory
publication date: 1991-01-01T00:00:00Z
review text: Let D be a symmetric domain in the complex plane with the Shilov boundary \(S_ D\) and let \(P: L^ 2(S_ D)\to H^ 2(S_ D)\) be the orthogonal projection onto the Hardy space. The author considers the Toeplitz operators \(T_ f\phi =P(f\phi),\phi \in H^ 2(S_ D)\), with matricial symbols f. He computes the K-groups of the \(C^*\)-algebra of these operators and obtains the theorem on Fredholmness and index of \(T_ f\). This theorem generalises the similar result for scalar-valued symbol, see \textit{C. A. Berger}, \textit{L. A. Coburn} and \textit{A. Coranyi}, C. R. Acad. Sci., Paris, Sér. A 290, 989-991 (1980; Zbl 0436.47021).
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 46L87
zbMATH DE Number: 4208850
zbMATH Keywords: Lie spheres
zbMATH Keywords: symmetric domain
zbMATH Keywords: Shilov boundary
zbMATH Keywords: orthogonal projection onto the Hardy space
zbMATH Keywords: Toeplitz operators
zbMATH Keywords: matricial symbols
zbMATH Keywords: K-groups
zbMATH Keywords: Fredholmness
zbMATH Keywords: index
reviewed by: S. G. Samko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208850