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

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

2011-10-31

arxiv.org/abs/1110.6858v1

Mathematics

Operator Algebras

9 pages; survey article on joint work with Pere Ara

Scientific paper

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.

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