فهرست نشریات علمی دسترسی آزاد ایران

Let $X$ be a compact Hausdorff space, $A$ be a (commutative) Banach algebra and $\mathcal{A}$ be a Banach $A$-valued function algebra on $X$. Let $\mathfrak{A}$ be the function algebra on $X$, consisting of scalar-valued functions in $\mathcal{A}$. We study and characterize various amenability properties of the algebra $\mathcal{A}$ in terms of cohomological properties of $\mathfrak{A}$ 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 $\mathfrak{A} \hat \otimes_\gamma A$. As consequences, some known results in this area are covered.