On some properties of CV_{(0)}(X, A)

Abstract

Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV₍₀₎(X, A) be the algebra of all weighted vector-valued continuous functions with the topology given by the uniform seminorms induced by V . In this paper we study some properties of A that are inherited by CV₍₀₎(X, A). These properties are related to the unit element, spectral seminorms and uniformly A-convex property.