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Derivations of subhomogeneous $ C^*$-algebras are implemented by local multipliers


Author: Ilja Gogić
Journal: Proc. Amer. Math. Soc. 141 (2013), 3925-3928
MSC (2010): Primary 46L57; Secondary 46L05
DOI: https://doi.org/10.1090/S0002-9939-2013-11762-4
Published electronically: July 23, 2013
MathSciNet review: 3091782
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Abstract: Let $ A$ be a subhomogeneous $ C^*$-algebra. Then $ A$ contains an essential closed ideal $ J$ with the property that for every derivation $ \delta $ of $ A$ there exists a multiplier $ a \in M(J)$ such that $ \delta =\mathrm {ad}(a)$ and $ \Vert\delta \Vert=2\Vert a\Vert$.


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Additional Information

Ilja Gogić
Affiliation: Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia
Email: ilja@math.hr

DOI: https://doi.org/10.1090/S0002-9939-2013-11762-4
Keywords: $C^*$-algebra, derivation, local multiplier algebra, subhomogeneous
Received by editor(s): January 18, 2012
Received by editor(s) in revised form: January 24, 2012
Published electronically: July 23, 2013
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.