Document Type : Revised File ( Second edition)


1 Faculty of Mathematics Science and Statistic‎, ‎Birjand University‎, ‎Birjand‎, ‎Iran

2 School of Mathematics and Computer Science‎, ‎Damghan University‎, ‎Damghan‎, ‎ Islamic Republic of Iran

3 3Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Islamic Republic of Iran


Let "S" be a commutative (not necessary unital) inverse semigroup with the set of idempotents E ‎then l^1 ("S") is a commutative Banach‎ l^1 ("E")-module with canonical actions‎. ‎Recently‎, ‎it is shown that the triangular Banach algebra T=Tri(l^1(S), M, l^1(S)) is ("n)" -weakly l^1 ("E")-module amenable‎, ‎provided that M=l^1 ("S") and "S" is unital or E satisfies condition D_k for some k∈N ‎. ‎In this paper‎, ‎we show that T is (2n+1)-weakly l^1 ("E")-module amenable‎, ‎without any additional conditions on" S" and E, ‎if M is a certain quotient space of l^1 ("S").