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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 language  English 

Pages (fromto)  93102 
Number of pages  10 
Journal  Operator Theory: Advances and Applications 
Volume  233 
Early online date  28 Sept 2013 
DOIs  
Publication status  Published  2013 
Keywords
 C*algebra
 Injective envelope
 Local multiplier algebra
 Sheaf theory
ASJC Scopus subject areas
 Analysis
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Dive into the research topics of 'The second local multiplier algebra of a separable C*algebra'. Together they form a unique fingerprint.
Derivations and Local Multipliers of C*Algebras
Martin Mathieu (Invited speaker)
19 Sept 2013Activity: Talk or presentation types › Invited talk

A New Formula for the Local Multiplier Algebra
Martin Mathieu (Keynote speaker)
28 Apr 2011Activity: Talk or presentation types › Invited or keynote talk at national or international conference

C*Algebras of Local Multipliers
Martin Mathieu (Invited speaker) & Armando R. Villena (Host)
24 Feb 2011Activity: Talk or presentation types › Invited talk