Fundamental approximate identities and quasi-multipliers of simple AF \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Fundamental approximate identities and quasi-multipliers of simple AF \(C^*\)-algebras
zbMATH Open document ID: 0678.46048
DOI: 10.1016/0022-1236(88)90028-6
author: Huaxin Lin
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: Let A be a \(C^*\)-algebra and \(A^{**}\) be its enveloping von Neumann algebra. An element \(x\in A^{**}\) is a multiplier of A if xa, ax\(\in A\) for all \(a\in A\), and x is a quasi-multiplier if axb\(\in A\) for all \(a,b\in A\). The author denoted the multipliers the left multipliers, the right multipliers and the quasi-multipliers by M(A), LM(A), RM(A) and QMA, respective. The question was raised by Akemann and Pedersen whether \(QM(A)=LM(A)+RM(A)\). L. G. Brown showed the relation between this problem and the problem of perturbations of \(C^*\)-algebras. This paper studies fundamental approximate identity as generation of stable \(C^*\)-algebras. Moreover the author answers the quasi multiplier question for separable simple AF \(C^*\)-algebras. He also finds applications to perturbation problems.
reviewed by: V. Ya. Golodets
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 4111349
zbMATH Keywords: enveloping von Neumann algebra
zbMATH Keywords: multiplier
zbMATH Keywords: fundamental approximate identity
zbMATH Keywords: stable \(C^*\)-algebras
zbMATH Keywords: quasi multiplier question
zbMATH Keywords: separable simple AF \(C^*\)-algebras
zbMATH Keywords: perturbation problems
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90028-6
OpenAlex ID: W2024182885
cites work: Complications of semicontinuity in \(C^*\)-algebra theory
cites work: Q5611281
cites work: Q3255627
cites work: Traces on simple AF C*-algebras
cites work: Q3670005
cites work: Perturbation of operator algebras
cites work: Near inclusions of C*-algebras
cites work: Scattered $C^*$-algebras.
cites work: Scattered $C^*$-algebras II.
cites work: Perturbations of Banach Algebras
cites work: A Counterexample in the Perturbation Theory of C*-Algebras
cites work: Perturbations of Von Neumann Algebras I Stability of Type
cites work: The Quasi-Multiplier Conjecture
cites work: Q3205815
description: scientific article; zbMATH DE number 4111349