Weight generalization of the space of continuous functions vanishing at infinity

Abstract

AbstractIn this paper, we characterize the weighted generalization of the space of continuous functions vanishing at infinity and correct some wrong results in the paper. Let X be a locally compact space and ν is an arbitrary weight (non‐negative function) on X. We give a correct and comprehensive definition of the weighted generalization of , and show that it is a seminormed space with respect to the canonical seminorm , where . We find conditions on ν under which , with respect to , becomes a normed space or a Banach space or an algebra, or a topological algebra, respectively.