ℕ-compactness and weighted composition maps

Abstract

Abstract. In this paper we study some conditions on (not necessarily continuous) linear maps T between spaces of real-or complex-valued continuous functions C(X) and C(Y ) which allow us to describe them as weighted composition maps. This description depends strongly on the topology in X; namely, it can be given when X is N-compact, but cannot in general if some kind of connectedness on X is assumed. Finally we also give an infimum-preserving version of the Banach-Stone theorem. The results are also proved for spaces of bounded continuous functions when K is a field endowed with a nonarchimedean valuation and it is not locally compact.