Generalizing the notion of left amenability for so-called F -algebras [ 12 ], we study the concept of ϕ-amenability of a Banach algebra A , where ϕ is a homomorphism from A to ℂ. We establish several characterizations of ϕ-amenability as well as some hereditary properties. In addition, some illuminating examples are given.
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Kaniuth et al. (2008) studied this question.