Amenability-like properties of C(X,A)

Abstract

Let A be a Banach algebra and X be a compact Hausdorff space. For given homomorphisms ? ? Hom(A) and ? ? Hom(C(X,A)), we introduce homomorphisms ?? ? Hom(C(X,A)) and ??x ? Hom(A), where x ? X. We then study both ??-(weak) amenability of C(X,A), and ?x-(weak) amenability of A.