Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2020; 35(3): 891-906

Online first article May 22, 2020      Printed July 31, 2020

https://doi.org/10.4134/CKMS.c200020

Copyright © The Korean Mathematical Society.

Module derivations on commutative Banach modules

Massoud Amini, Abasalt Bodaghi, Behrouz Shojaee

Tarbiat Modares University; Islamic Azad University; Islamic Azad University

Abstract

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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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