TY - JOUR ID - 1767 TI - $\varphi$-CONNES MODULE AMENABILITY OF DUAL BANACH ALGEBRAS JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Ghaffari, A. AU - Javadi Syahkale, S. AU - Tamimi, E. AD - Department of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan, Iran. AD - Faculty of Engineering- East Guilan, University of Guilan, P.O. Box 44891-63157, Rudsar, Iran. Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 69 EP - 82 KW - banach algebras KW - module amenability KW - derivation KW - semigroup algebra DO - 10.22044/jas.2019.8503.1415 N2 - In this paper we define $\varphi$-Connes module amenability ofa dual Banach algebra $\mathcal{A}$ where $\varphi$ is a bounded $w_{k^*}$-modulehomomorphism from $\mathcal{A}$ to $\mathcal{A}$. We are mainlyconcerned with the study of $\varphi$-module normalvirtual diagonals. We show that if $S$ is a weakly cancellativeinverse semigroup with subsemigroup $E$ of idempotents, $\chi$is a bounded $w_{k^*}$-module homomorphism from $l^1(S)$ to $l^1(S)$ and $l^1(S)$as a Banach module over $l^1(E)$ is $\chi$-Connes module amenable, then it has a $\chi$-module normal virtualdiagonal. In the case $\chi=id$, the converse holds UR - https://jas.shahroodut.ac.ir/article_1767.html L1 - https://jas.shahroodut.ac.ir/article_1767_75ba3bc94de55cd62417dc2836015b68.pdf ER -