Document Type : Revised File ( Second edition)
Authors
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
Abstract
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").
Keywords