Amenability as a hereditary property in some algebras of vector-valued functions
Terje Hõim, D. Robbins · Contemporary mathematics - American Mathematical Society · 2015
If A A is an amenable Banach algebra and X X is a compact Hausdorff space, then it is well-known that C ( X , A ) , C(X,A), the space of continuous A A -valued functions on X , X, is also amenable. Likewise, if { A x : x ∈ X } \{A_{x}:x\in X\} is a collection of amenable Banach algebras which satisfy a certain uniformity condition, then the c 0 c_{0} -sum B B of the A x , A_{x}, is also amenable. Both C ( X , A ) C(X,A) and B B are C ( X ) C(X) -modules in an evident fashion, and both inherit their amenability (from A A and the A x ) .