Let B be an abstract Segal algebra with respect to A. For a nonzero character φ on A, we study φ-amenability, and φ-contractibility of A and B. We then apply these results to abstract Segal algebras related to locally compact groups.2000 Mathematics subject classification: primary 46H05; secondary 43A07.
Let A be a Banach algebra and let φ be a nonzero character on A. We give some necessary and sufficient conditions for the left φ-contractibility of A as well as several hereditary properties. We also study relations between homological properties of some Banach left A-modules, the left φ-contractibility and the right φ-amenability of A. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.
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