Topological algebras and Mackey topologies

Abstract:

Let E be a locally m-convex algebra with dual space $E’$. In a recent paper S. Warner asked if the finest locally m-convex topology on E compatible with $E’$ 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 ${C_b}(S)$ with the strict topology.