The Arens product in locally convex algebras. (Spanish: El Producto de Arens en álgebras localmente convexas).

Abstract

The author considers locally convex algebras. He defines an Arens product for such algebras and applies it to obtain various generalizations of results known for Banach algebras. He gives a necessary and sufficient condition for the existence of an approximate identity and, for a locally convex algebra with an approximate right identity, he gives a necessary and sufficient condition for the existence of a right identity. He shows that an element x≠0 is a right topological divisor of zero if and only if it is a right divisor of zero when considered as an element of the bidual space.