in this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric connes amenability. we determine symmetric module amenability and symmetric connes amenability of some concrete banach algebras. indeed, it is shown that $ell^1(s)$ is  a symmetric $ell^1(e)$-module amenable if and only if $s$ is amenable, where $s$ is an inverse semigroup with subsemigr...

Ideal Connes-amenability of dual Banach algebras was investigated in [17] by A. Minapoor, A. Bodaghi and D. Ebrahimi Bagha. They studied weak∗continuous derivations from dual Banach algebras into their weak∗-closed two- sided ideals. This work considers weak∗-continuous derivations of dual triangular Banach algebras into their weak∗-closed two- sided ideals . We investigate when weak∗continuous...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...

in this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (k, ?) are equivalent. for a normal subgroup h of k, we define a weight function ?? on kih and obtain connection between left amenability of (k, ?) and (k|h, ??). let h be a compact subhypergroup of k. we define the weight function on k||h and obtain connection betw...