Open AccessWeak module amenability for the second dual of a Banach algebra
Author(s) -
Shabani Soltanmoradi,
Davood Ebrahimi Bagha,
Pourbahri Rahpeyma
Publication year - 2021
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.276
H-Index - 6
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2021.25.19
Subject(s) - banach algebra , dual (grammatical number) , mathematics , pure mathematics , algebra over a field , discrete mathematics , banach space , art , literature
In this paper we study the weak module amenability of Banach algebras which are Banach modules over another Banach algebra with compatible actions. We show that for every module derivation D : A ↦ ( A/J_A )∗ if D∗∗(A∗∗) ⊆ WAP (A/J_A ), then weak module amenability of A∗∗ implies that of A. Also we prove that under certain conditions for the module derivation D, if A∗∗ is weak module amenable then A is also weak module amenable.