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Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras

Author: Ebrahim Samei
Journal: Proc. Amer. Math. Soc. 133 (2005), 229-238
MSC (2000): Primary 46L07, 47B47
Published electronically: July 26, 2004
MathSciNet review: 2085174
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Abstract: We show that for a locally compact group $G$, every completely bounded local derivation from the Fourier algebra $A(G)$ into a symmetric operator $A(G)$-module or the operator dual of an essential $A(G)$-bimodule is a derivation. Moreover, for amenable $G$ we show that the result is true for all operator $A(G)$-bimodules. In particular, we derive a new proof to a result of N. Spronk that $A(G)$ is always operator weakly amenable.

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Additional Information

Ebrahim Samei
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2

Keywords: Local derivations, Fourier algebra, operator space, operator weak amenability
Received by editor(s): June 13, 2003
Received by editor(s) in revised form: September 30, 2003
Published electronically: July 26, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society

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