Band-dominated Fredholm operators on discrete groups
type: Item
instance of: scholarly article
title: Band-dominated Fredholm operators on discrete groups
zbMATH Open document ID: 1085.47061
author: John Roe
published in: Integral Equations and Operator Theory
publication date: 2005-04-29T00:00:00Z
review text: \textit{V.\ S.\ Rabinovich, S.\ Roch} and \textit{B.\ Silbermann} [Integral Equations Oper.\ Theory 40, No.~3, 342--381 (2001; Zbl 1032.47051)] considered the \(C^{\ast}\)-algebra of band-dominated operators with operator-valued coefficients, a class of operators on the Hilbert space \(\ell^{2} (\mathbb{Z}^{n})\). They built a symbol calculus which provides a theoretical answer to the question whether or not a band-dominated operators is Fredholm. In the paper under review, the author extends the main results of the symbol calculus of [loc.~cit.] in the Hilbert space case. He replaces the group \(\mathbb{Z}^{n}\) by any finitely generated discrete group \(\Gamma\) which is exact in the sense of \(C^{\ast}\)-algebra theory.
reviewed by: Antonio M. Peralta
Mathematics Subject Classification ID: 47L80
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 2162377
zbMATH Keywords: band-dominated Fredholm operators with operator-valued coefficients
zbMATH Keywords: \(\ell^{2} (\mathbb{Z}^{n})\)
MaRDI profile type: Publication
full work available at URL: s00020-004-1326-4
OpenAlex ID: W1974233217
DOI: 10.1007/S00020-004-1326-4
description: scientific article; zbMATH DE number 2162377