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Keywords:
Banach algebra; $(\varphi ,\psi )$-derivation; group algebra; locally compact group; measure algebra; Segal algebra; weak amenability
Banach algebra; $(\varphi ,\psi )$-derivation; group algebra; locally compact group; measure algebra; Segal algebra; weak amenability
Summary:
The generalized notion of weak amenability, namely $(\varphi ,\psi )$-weak amenability, where $\varphi ,\psi $ are continuous homomorphisms on a Banach algebra ${\mathcal A}$, was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the $(\varphi ,\psi )$-weak amenability on the measure algebra $M(G)$, the group algebra $L^1(G)$ and the Segal algebra $S^1(G)$, where $G$ is a locally compact group, are studied. As a typical example, the $(\varphi ,\psi )$-weak amenability of a special semigroup algebra is shown as well.
References:
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