An index theorem for Toeplitz operators with noncommutative symbol space
type: Item
instance of: scholarly article
title: An index theorem for Toeplitz operators with noncommutative symbol space
zbMATH Open document ID: 0815.47033
author: John Phillips
author: Iain Raeburn
published in: Journal of Functional Analysis
publication date: 1994-07-04T00:00:00Z
full work available at URL: http://hdl.handle.net/1828/2734
review text: The authors consider Toeplitz operators with symbol in a \(C^*\)-algebra \(A\) carrying an action \(\alpha\) of \(\mathbb{R}\). They prove that when \(A\) has an \(\mathbb{R}\)-invariant trace \(\tau\), the Toeplitz operators with invertible symbols are Fredholm elements of an appropriate von Neumann algebra, and give a formula for their Breuer index in terms of \(\tau\) and the infinitesimal generator of the one-parameter automorphism group \(\alpha\). This theorem includes as special cases recent results of Curto-Muhly-Xia, Ji, and Lesch, as well as classical results of Gohberg-Krein and Coburn- Douglas-Schaeffer-Singer, and provides a more direct approach to the corresponding index theorems for systems.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 599765
zbMATH Keywords: invariant trace
zbMATH Keywords: Toeplitz operators with symbol in a \(C^*\)-algebra
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: Breuer index
zbMATH Keywords: infinitesimal generator
zbMATH Keywords: one-parameter automorphism group
zbMATH Keywords: index theorems for systems
MaRDI profile type: Publication
OpenAlex ID: W2021187667
DOI: 10.1006/JFAN.1994.1032
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description: scientific article; zbMATH DE number 599765