The local multiplier algebra of a C\(^*\)-algebra. II
type: Item
instance of: scholarly article
title: The local multiplier algebra of a C\(^*\)-algebra. II
zbMATH Open document ID: 0964.43003
published in: Journal of Functional Analysis
publication date: 2001-02-20T00:00:00Z
review text: [Part I by the author in Q. J. Math., Oxford (2) 47, No. 185, 123-132 (1996; Zbl 0857.43004).] Let \(A\) be a separable \(C^*\)-algebra and let \(M_{\text{loc}}(A)\) be its local multiplier algebra. It is shown that every minimal closed prime ideal of \(M_{\text{loc}}(A)\) is primitive. If the primitive ideal space of \(A\) has a dense \(G_\delta\) consisting of closed points (in particular, \(\text{Prim}(A)\) is a \(T_1\) space) and \(A\) is unital, then \(M_{\text{loc}}(A)\) is its own multiplier algebra and has only inner derivations.
Mathematics Subject Classification ID: 43A22
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1437355
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: local multiplier algebra
author: Douglas W. B. Somerset
reviewed by: Khristo N. Boyadzhiev
MaRDI profile type: Publication
full work available at URL: jfan.2000.3527
OpenAlex ID: W1985169588
cites work: Derivations of non-separable \(C^*\)-algebras
cites work: Central Sequences and Inner Derivations of Separable C ∗ -Algebras
cites work: Multipliers of C -algebras
cites work: A local version of the Dauns-Hoffmann theorem
cites work: AN APPLICATION OF LOCAL MULTIPLIERS TO CENTRALIZING MAPPINGS OF C*-ALGEBRAS
cites work: A simple local multiplier algebra
cites work: Q4780925
cites work: Note on Lattice Points in Star Domains
cites work: Double Centralizers and Extensions of C ∗ -Algebras
cites work: Non Commutative Integration for Monotone Sequentially Closed $C^*$ Algebras.
cites work: Sur Les Espaces Localement Quasi-Compacts
cites work: Q4150220
cites work: Automorphisms determined by multipliers on ideals of a \(C^*\)-algebra
cites work: Some C*-algebras with outer derivations, III
cites work: A Stone-Weierstrass theorem for \(C^*\)-algebras
cites work: Irreducible Module Homomorphisms of a Von Neumann Algebra into its Center
cites work: The Centre of the Regular Monotone Completion of a C∗ -Algebra
cites work: \(AW^*\)-algebras are \(QW^*\)-algebras
cites work: Q5541832
cites work: On a weakly central operator algebra
cites work: Groups with \(T_1\) primitive ideal spaces
cites work: Derivations of AW\(^*\)-algebras are inner
cites work: Derivations of C\(^*\)-algebras have semi-continuous generators
cites work: Q4293544
cites work: Q3205815
cites work: Approximating derivations on ideals of \(C^*\)-algebras
cites work: Multipliers of \(AW^*\)-algebras
cites work: Simple quotients of group $C^*$-algebras for two step nilpotent groups and connected Lie groups
cites work: Derivations of Quotients of Von Neumann Algebras
cites work: A Structure Theory in the Regular δ-Completion of C -Algebras
cites work: Derivations of simple $C^*$-algebras. II
cites work: Q4876288
cites work: Sums of Subalgebras of C (X )
cites work: Q4741226
cites work: On the Homomorphic Image of the Center of a $C^*$-Algebra.
cites work: Every Monotone σ-Complete C* -Algebra is the Quotient of its Baire* Envelope by a Two Sided σ-Ideal
cites work: Regular σ-Completions of C*-Algebras
DOI: 10.1006/JFAN.2000.3527
description: scientific article; zbMATH DE number 1437355