The kernel and continuity ideals of homomorphisms from C_0(\Omega)

TL;DR

This paper characterizes the continuity ideals and kernels of homomorphisms from algebras of continuous functions on locally compact spaces into Banach algebras, providing a structural understanding of these mappings.

Contribution

It offers a new description of the continuity ideals and kernels of such homomorphisms, advancing the theoretical understanding of these algebraic structures.

Findings

Describes the structure of continuity ideals.

Characterizes kernels of homomorphisms.

Provides a framework for analyzing function algebra homomorphisms.

Abstract

We give a description of the continuity ideals and the kernels of homomorphisms from the algebras of continuous functions on locally compact spaces into Banach algebras.