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\(l^1\)-Munn ideal amenability of certain semigroup algebras. (English) Zbl 1289.43001

A Banach algebra \(A\) is called ideally amenable, if for every closed ideal \(I\) of \(A\), the first cohomology group of \(A\) with coefficients in \(I^*\) is trivial.
The author investigates the ideal amenability of \(l^1(G_p)\) where \(G_p\) is a maximal subgroup of an inverse semigroup. In particular, the case of Rees matrix semigroups is considered. The method is based on the theory of matrix algebras with arbitrary index sets; see G. H. Esslamzadeh [J. Funct. Anal. 161, No. 2, 364–383 (1999; Zbl 0927.46027)].

MSC:

43A07 Means on groups, semigroups, etc.; amenable groups

Citations:

Zbl 0927.46027
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