A remark on the extension of a class of linear functionals

TL;DR

This paper discusses an extension method for positive linear functionals defined on subalgebras of continuous functions over subsets of , contributing to the understanding of functional extension in functional analysis.

Contribution

It introduces a new approach for extending positive linear functionals on subalgebras of continuous functions.

Findings

Extended linear functionals preserve positivity.

Provides conditions for the extension to exist.

Enhances the theoretical framework of functional analysis.

Abstract

We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.