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.
Mathematics Subject Classification (2010).Primary 46L05. Secondary 46L06, 46M20.
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This paper is dedicated to Victor Shulman on his 65th birthday.
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Mathieu, M. (2014). The Second Local Multiplier Algebra of a Separable C*-algebra. In: Todorov, I., Turowska, L. (eds) Algebraic Methods in Functional Analysis. Operator Theory: Advances and Applications, vol 233. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0502-5_7
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DOI: https://doi.org/10.1007/978-3-0348-0502-5_7
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0501-8
Online ISBN: 978-3-0348-0502-5
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