The ideal structure of Toeplitz algebras
type: Item
instance of: scholarly article
title: The ideal structure of Toeplitz algebras
zbMATH Open document ID: 1069.46034
author: Sriwulan
author: Iain Raeburn
author: Sriwulan Adji
published in: Integral Equations and Operator Theory
publication date: 2004-09-22T00:00:00Z
review text: The authors study the algebra \({\mathcal T}(\Gamma)\subset B(\ell^2(\Gamma^+)\) generated by isometries of a totally ordered Abelian group \(\Gamma\), defined on the standard basis as shifts \(Z_xe_y=e_{x+y}\), \(x\in\Gamma^+\). The structure of ideals is well known when either \(\Gamma\subset\mathbb{R}\) or \(\Gamma\) is finitely generated. The problem of describing the ideal structure for a non-finitely generated totally ordered group is considered. A parametrization by \(X\) of the set of primitive ideals of the totally ordered set \(\Sigma(\Gamma)\) of ordered ideals \({\mathcal T}(\Gamma)\) is described. Also the hull-kernel topology on \(X\) is identified when the chain of order ideals in \(\Gamma\) is isomorphic to a subset of \(\{-\infty\}\cup\mathbb{Z}\cup\{\infty\}\).
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 20K30
zbMATH DE Number: 2101681
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: abelian group
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: ideals
reviewed by: Roland Duduchava
MaRDI profile type: Publication
full work available at URL: s00020-001-1174-4
OpenAlex ID: W2053327212
DOI: 10.1007/S00020-001-1174-4
description: scientific article; zbMATH DE number 2101681