Character contractibility of Banach algebras and homological properties of Banach modules
Volume 202 / 2011
Studia Mathematica 202 (2011), 205-225
MSC: Primary 46H25, 43A07; Secondary 22D15, 46H05.
DOI: 10.4064/sm202-3-1
Abstract
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.
