A strict topology for some weighted spaces of continuous functions

Abstract

In the classical case the strict topology introduced by Buck [2] on the space of bounded continuous scalar valued functions on the locally compact Hausdorff space X is given by the system W of all weights on X that vanish at infinity. The -bounded subsets of are exactly the norm bounded subsets, and is the finest locally convex topology which coincides on the norm bounded subsets with the compact open topology (cf. Dorroh [4]). Especially we have that holds algebraically. In this note we want to describe for an arbitrary system of weights V an associated system of weights W such that at least in many cases, including the classical one, the connection between and is the same as in the classical case.