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

Martin Mathieu

doi:10.1007/978-3-0348-0502-5_7

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

Martin Mathieu^*

^*Corresponding author for this work

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

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 (from-to)	93-102
Number of pages	10
Journal	Operator Theory: Advances and Applications
Volume	233
Early online date	28 Sept 2013
DOIs	https://doi.org/10.1007/978-3-0348-0502-5_7
Publication status	Published - 2013

Keywords

C*-algebra
Injective envelope
Local multiplier algebra
Sheaf theory

ASJC Scopus subject areas

Analysis

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10.1007/978-3-0348-0502-5_7Licence: Unspecified

Cite this

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KW - Sheaf theory

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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Derivations and Local Multipliers of C*-Algebras

A New Formula for the Local Multiplier Algebra

C*-Algebras of Local Multipliers

Cite this

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Activities

Derivations and Local Multipliers of C*-Algebras

A New Formula for the Local Multiplier Algebra

C*-Algebras of Local Multipliers

Cite this