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 \({\mathcal {B}},\) by the fundamental system of seminorms of a locally convex subalgebra \(({\mathcal {A},p}_\alpha )\). Moreover, we investigate when \({\mathcal {B}}\) is a locally convex algebra with respect to these topologies. Furthermore, we generalize an essential result related to derivations, from Banach to the Frechet case. Finally we provide a useful example in this field.