Module derivations on commutative Banach modules
Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 891-906
Published online May 22, 2020
Printed July 31, 2020
Massoud Amini, Abasalt Bodaghi, Behrouz Shojaee
Tarbiat Modares University; Islamic Azad University; Islamic Azad University
Abstract : In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup $S$, every module derivation of $l^1(S)$ into a reflexive module is inner.
Keywords : Banach module, inverse semigroup, module amenability, module derivation
MSC numbers : 46H25, 22D15, 43A20
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