Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani¹ ; Sima Soltani Renani¹

¹Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156-83111, Iran

Studia Mathematica, Tome 202 (2011) no. 3, pp. 205-225

Résumé

Let ${\cal A}$ be a Banach algebra and let $\phi$ be a nonzero character on ${{\cal A}}$. We give some necessary and sufficient conditions for the left $\phi$-contractibility of ${\cal A}$ as well as several hereditary properties. We also study relations between homological properties of some Banach left ${\cal A}$-modules, the left $\phi$-contractibility and the right $\phi$-amenability of ${\cal A}$. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Détail

DOI : 10.4064/sm202-3-1

Keywords: cal banach algebra phi nonzero character cal necessary sufficient conditions phi contractibility cal several hereditary properties study relations between homological properties banach cal modules phi contractibility right phi amenability nbsp cal finally characterize character contractibility various banach algebras related locally compact groups