On pseudo-contractibility of certain algebras related to a discrete semigroup

In this paper, we introduce a notion of ultra central approximate identity for Banach algebras which is a generalization of the bounded approximate identity and the central approximate identity. Using this concept we study pseudo-contractibility of some matrix algebras among \ell^۱-Munn algebras. As an application, for the Brandt semigroup S=M^{۰}(G,I) over a non-empty set I, we show that \ell^{۱}(S) has an ultra central approximate identity if and only if I is finite. Also we show that the notion of pseudo-contractibility and contractibility are the same on \ell^{۱}(S)^{**}, where S is the Brandt semigroup.

کلیدواژه ها:

Semigroup algebras ، Ultra central approximate identity ، Locally finite inverse semigroup ، Pseudo-contractibility ، Matrix algebras