Zahra Hasanzadeh - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Amin Mahmoodi - Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

In this paper,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability 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.

$sigma$-Connes amenability, Pseudo-amenability, Pseudo-Connes amenability, Beurling algebras