Amenability-Like properties of C(X,A)

Abstract

Let $A$ be a Banach algebra and $X$ be a compact Hausdorff space. Given homomorphisms $\sigma \in Hom(A)$ and $\tau \in Hom(C(X,A))$, we introduce induced homomorphisms $\tilde{\sigma }\in Hom(C(X,A))$ and $\tilde{\tau }\in Hom(A)$, respectively. We study when $\tau$-(weak) amenability of $C(X,A)$ implies $\tilde{\tau }$-(weak) amenability of $A$. We also investigate where $\sigma$-weak amenability of $A$ yields $\tilde{\sigma }$-weak amenability of $C(X,A)$.

References in corpus (1)

• Amenability properties of Banach algebra valued continuous functions