Toeplitz operators on symmetric Siegel domains
type: Item
instance of: scholarly article
title: Toeplitz operators on symmetric Siegel domains
zbMATH Open document ID: 0565.47016
DOI: 10.1007/BF01456076
author: Harald Upmeier
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163976
review text: In this paper, the structure theory for Toeplitz \(C^*\)-algebras over bounded symmetric domains in \({\mathbb{C}}^ n\) [cf. \textit{H. Upmeier}, Ann. Math., II. Ser. 119, 549-576 (1984; Zbl 0549.46031)] is applied to study smooth Toeplitz operators on the distinguished boundary \(\Sigma\) of a symmetric Siegel domain D. As the main result, it is shown that the \(C^*\)-algebra \({\mathcal T}_{\Sigma}\) generated by these operators is solvable of length \(r=rank(D)\) and that its irreducible representations correspond to the boundary components of D. This applies in particular to Wiener-Hopf operators on self-dual homogeneous cones, first studied by \textit{P. S. Muhly} and \textit{J. N. Renault} [Trans. Am. Math. Soc. 274, 1- 44 (1982; Zbl 0509.46049)].
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 3901472
zbMATH Keywords: structure theory for Toeplitz \(C^*\)-algebras over bounded symmetric domains
zbMATH Keywords: smooth Toeplitz operators
zbMATH Keywords: symmetric Siegel domain
zbMATH Keywords: Wiener-Hopf operators on self-dual homogeneous cones
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3901472