Applications of Asymptotic Riesz Representation Theorem

TL;DR

This paper reviews the connection between asymptotic spectral measures and positive asymptotic morphisms on locally compact spaces, highlighting applications of the asymptotic Riesz representation theorem.

Contribution

It provides a comprehensive review of the asymptotic Riesz representation theorem and discusses its applications in the context of spectral measures and morphisms.

Findings

Clarifies the relationship between spectral measures and asymptotic morphisms

Highlights applications of the asymptotic Riesz representation theorem

Provides insights into the structure of asymptotic spectral measures

Abstract

We review the relation between compact asymptotic spectral measures and certain positive asymptotic morphism on locally compact spaces via asymptotic Riesz representation theorem, as introduced by Martinez and Trout [3]. Applications to this theorem will be discus.