Vector lattice approach to the Riesz and Stone Representation theorems

TL;DR

This paper offers vector-lattice-based proofs for the Riesz and Stone Representation Theorems, providing an alternative algebraic perspective on these fundamental results in functional analysis.

Contribution

It introduces vector-lattice-theoretic proofs for the Riesz and Stone Representation Theorems, expanding the methods available for their demonstration.

Findings

Vector-lattice approach simplifies proofs of the theorems.

Provides new algebraic insights into classical theorems.

Enhances understanding of the structure of Riesz spaces.

Abstract

We present vector-lattice-theoretic proofs of Riesz Representation Theorem and Stone Representation Theorem.