The second local multiplier algebra of a separable C*-algebra

Martin Mathieu*

*Corresponding author for this work

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)93-102
Number of pages10
JournalOperator Theory: Advances and Applications
Volume233
Early online date28 Sep 2013
DOIs
Publication statusPublished - 01 Jan 2014

Keywords

  • C*-algebra
  • Injective envelope
  • Local multiplier algebra
  • Sheaf theory

ASJC Scopus subject areas

  • Analysis

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