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

Samei, Ebrahim

doi:10.1090/S0002-9939-04-07555-0

Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras
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Proc. Amer. Math. Soc. 133 (2005), 229-238 Request permission

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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