$\varphi$-CONNES MODULE AMENABILITY OF DUAL BANACH ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| مقاله 7، دوره 8، شماره 1، آذر 2020، صفحه 69-82 اصل مقاله (169.7 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8503.1415 | ||
| نویسندگان | ||
| A. Ghaffari* 1؛ S. Javadi Syahkale2؛ E. Tamimi1 | ||
| 1Department of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan, Iran. | ||
| 2Faculty of Engineering- East Guilan, University of Guilan, P.O. Box 44891-63157, Rudsar, Iran. | ||
| چکیده | ||
| In this paper we define $\varphi$-Connes module amenability of a dual Banach algebra $\mathcal{A}$ where $\varphi$ is a bounded $w_{k^*}$-module homomorphism from $\mathcal{A}$ to $\mathcal{A}$. We are mainly concerned with the study of $\varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse 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 virtual diagonal. In the case $\chi=id$, the converse holds | ||
| کلیدواژهها | ||
| Banach algebras؛ module amenability؛ derivation؛ semigroup algebra | ||
| مراجع | ||
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