The Second Local Multiplier Algebra of a Separable C*-algebra

DOI10.1007/978-3-0348-0502-5_7zbMATH Open1325.46059arXiv1110.6858OpenAlexW2122368703MaRDI QIDQ5244883

Martin Mathieu

Publication date: 31 March 2015

Published in: Operator Theory: Advances and Applications (Search for Journal in Brave)

Abstract: Several examples of (separable) C*-algebras with the property that their second (iterated) local multiplier algebra is strictly larger than the first have been found by various groups of authors over the past few years, thus answering a question originally posed by G. K. Pedersen in 1978. This survey discusses a systematic approach by P. Ara and the author to produce such examples on the one hand; on the other hand, we present new criteria guaranteeing that the second and the first local multiplier algebra of a separable C*-algebra agree. For this class of C*-algebras, each derivation of the local multiplier algebra is inner.

Full work available at URL: https://arxiv.org/abs/1110.6858

zbMATH Keywords

\(C^{\ast}\)-algebraderivationsheaf theoryinjective envelopelocal multiplier algebra

Mathematics Subject Classification ID

Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) General theory of (C^*)-algebras (46L05) Research exposition (monographs, survey articles) pertaining to functional analysis (46-02) Tensor products of (C^*)-algebras (46L06)

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The local multiplier algebra of a \(C^\ast\)-algebra with finite dimensional irreducible representations

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