amenability properties of vector-valued function algebras

Let x be a compact hausdorff space, a be a (commutative) banach algebra and a be a banach a-valued function algebra on x. let a be the function algebra on x, consisting of scalar-valued functions in a. we study and characterize various amenability properties of the algebra a in terms of cohomological properties of a and a. containing some well-known examples, such as c (x, a) and lip(x, a), the class of vector-valued function algebras also includes, in some sense, the tensor products a⊗ˆ γa. as consequences, some known results in this area are covered.