Topological algebras and Mackey topologies

Abstract

Let E be a locally m-convex algebra with dual space E ′ E’ . In a recent paper S. Warner asked if the finest locally m-convex topology on E compatible with E ′ E’ was the mackey topology. It is shown that this is not the case. A similar result is given for this question in the A-convex algebra case. For any A-convex algebra, a construction is given of an associated locally m-convex algebra. It is shown that this associated locally m-convex topology is always the compact-open topology for the space C b ( S ) {C_b}(S) with the strict topology.