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.
Massoud Amini, Abasalt Bodaghi, Behrouz Shojaee
Tarbiat Modares University; Islamic Azad University; Islamic Azad University
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
2019; 34(3): 743-755
2023; 38(4): 1101-1110
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