$sigma$Connes Amenability and Pseudo(Connes) Amenability of Beurling Algebras

In this paper,  pseudoamenability and pseudoConnes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudoConnes amenability and pseudoamenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.