A. Mahmoodi

Amenability-Like properties of C(X,A)

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