CHARACTER AMENABILITY AND CHARACTER PSEUDO-AMENABILITY OF CERTAIN BANACH ALGEBRAS

In this paper, we study character amenability of semi-group algebras ℓ^1(S) and weighted semi-group algebras ℓ^1(S,ω), for a certain semi-groups such as right(left) zero semigroup, rectangular band semi-group, band semi-group and uniformly locally finite inverse semi-group. In particular, we show that for a right (left) zero semi-group or a rectangular band semi-group, character amenability, amenability, pseudo - amenability of ℓ^1(S, ω), for each weight ω, are equivalent. We also show that for an Archimedean semi-group S, character pseudo - amenability, amenability, approximate amenability and pseudo-amenable of ℓ^1(S) are equivalent.