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Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras
Authors:Ebrahim Samei
Affiliation:Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
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.

Keywords:Local derivations   Fourier algebra   operator space   operator weak amenability
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