An index theorem for multivariable Toeplitz operators
type: Item
instance of: scholarly article
title: An index theorem for multivariable Toeplitz operators
zbMATH Open document ID: 0589.47029
DOI: 10.1007/BF01199351
author: Harald Upmeier
published in: Integral Equations and Operator Theory
publication date: 1986-01-01T00:00:00Z
review text: The structure theory of the Toeplitz \(C^*\)-algebra \({\mathcal T}\) over a bounded symmetric domain D of rank r [cf. \textit{H. Upmeier}, Ann. Math., II. Ser. 119, 549-576 (1984; Zbl 0549.46031)] implies that there exist r analytical Fredholm indices for operators in \({\mathcal T}\), which are in general K-theory valued and ''live'' on the strata of the boundary of D. In this paper a topological formula for the ''highest'' r-index is given, using the Bott element of certain sphere bundles defined in Jordan algebraic terms. More recently, the author found topological index formula for al j-indices (1\(\leq j\leq r)\), in particular for the usual integer-valued (1-) index.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 3946966
zbMATH Keywords: Toeplitz \(C^*\)-algebra
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: analytical Fredholm indices
zbMATH Keywords: Bott element
zbMATH Keywords: sphere bundles defined in Jordan algebraic terms
zbMATH Keywords: topological index formula
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01199351
OpenAlex ID: W4240782674
description: scientific article; zbMATH DE number 3946966