On saturated uniformly A-convex algebras

TL;DR

This paper introduces a new class of saturated uniformly A-convex algebras, extending the concept of A-convexity with a focus on their topological properties, inspired by Cochran's ideas.

Contribution

It provides a formal definition of saturated uniformly A-convex algebras and explores their properties, especially in the m-convex case, linking them to uniform topological algebras.

Findings

Saturated uniformly A-convex algebras are characterized within the m-convex framework.

In the m-convex case, such algebras are shown to be uniform topological algebras.

Abstract

Following ideas of A.C.Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.