On some automatic continuity theorems

TL;DR

This paper characterizes certain classes of topological algebras using multiplicative linear functionals and extends automatic continuity theorems to broader algebra classes, with various applications.

Contribution

It introduces new characterizations of uniform and saturated locally multiplicatively convex algebras and extends automatic continuity theorems to a larger algebra class.

Findings

Characterizations of unital uniform topological algebras

Extension of automatic continuity theorems

Applications to broader algebra classes

Abstract

We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform topological algebras are extended to a larger class of algebras. Consequences and applications are given.