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http://dx.doi.org/10.4134/CKMS.c200020

MODULE DERIVATIONS ON COMMUTATIVE BANACH MODULES  

Amini, Massoud (Department of Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
Bodaghi, Abasalt (Department of Mathematics Garmsar Branch Islamic Azad University)
Shojaee, Behrouz (Department of Mathematics Karaj Branch Islamic Azad University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 891-906 More about this Journal
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 𝑙1(S) into a reflexive module is inner.
Keywords
Banach module; inverse semigroup; module amenability; module derivation;
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Times Cited By KSCI : 2  (Citation Analysis)
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