Abstract
Let \(K\) be a locally compact Hausdorff space and let \(X\) be a Banach space. By \(C_0(K, X)\) we denote the Banach space of all \(X\)-valued continuous functions on \(K\) that vanish at infinity, equipped with the supremum norm. When \(K\) is compact, we write \(C(K, X)\). In this context, the spaces \(C(K)\), where \(X\) is the scalar field, play a central role in the theory of Bana…