Character contractibility of Banach algebras and homological properties of Banach modules

Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani

 Sima Soltani Renani (Isfahan)

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