On the strict, uniform and compact-open topologies on an algebra

Abstract

We introduce and study strict, uniform, and compact-open locally convex topologies on an algebra B, by the fundamental system of seminorms of a locally convex subalgebra (A, pα). Moreover, we investigate when B is a locally convex algebra with respect to these topologies. Furthermore, we generalize an essential result related to derivations, from Banach to the Fréchet case. Finally we provide a useful example in this field. © 2017, Akadémiai Kiadó, Budapest, Hungary.