Non-maximal closed prime ideals in a unital commutative Banach algebra are accessible
Functional Analysis
2025-05-09 v1
Abstract
It is proved that in a commutative unital Banach algebra, every non-maximal closed prime ideal is accessible. Specifically, it can be represented as the intersection of all closed ideals of the algebra that properly contain it. Consequently, all derivations and epimorphisms on commutative unital semi-prime Banach algebras are continuous. Moreover, any separating ideal in a commutative unital Banach algebra is nilpotent and, therefore, a nil ideal.
Cite
@article{arxiv.2505.04849,
title = {Non-maximal closed prime ideals in a unital commutative Banach algebra are accessible},
author = {Ramesh Garimella},
journal= {arXiv preprint arXiv:2505.04849},
year = {2025}
}