Pseudo-amenability and Biflatness of weighted algebras and their second dual on inverse semigroups

This paper proves that when S is an inverse semigroup, pseudo- menability, amenability and approximately amenability of \ell^{۱}(S, \omega) are equivalent, E(S) is finite and every maximal subgroup of S is amenable.In addition, for a discrete inverse semigroup of S, we prove when (E(S),\leq) is niformly locally finite, then \ell^{۱}(S, \omega)^{**} is pseudo-amenable if and only if \ell^{۱}(S) , it is pseudo-amenable and S is finite.Also , we prove that for discrete inverse semigroup S, if \ell^{۱}(S, \omega) has a bounded approximate identity then \ell^{۱}(S, \omega)^{**} is amenable if and only if \ell^{۱}(S) is biprojective and S is finite. Also, we show that for an Archimedean semigroup S, if \Omega be bounded on every maximal subgroup G of S, pseudo-amenability,amenability and approximate amenability of \ell^{۱}(S, \omega) are equivalent, and also if S be a weakly cancellative commutative semigroup, we obtain some results on pseudo-amenability of the second dual of \ell^{۱}(S, \omega) .

کلیدواژه ها:

biprojective ، archimedean semigroup ، weakly cancellative commutative semigroup