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 , every completely bounded local derivation from the Fourier algebra into a symmetric operator -module or the operator dual of an essential -bimodule is a derivation. Moreover, for amenable we show that the result is true for all operator -bimodules. In particular, we derive a new proof to a result of N. Spronk that is always operator weakly amenable.