Eigenfunctionals for positive operators

TL;DR

This paper introduces an eigenfunctional theorem for positive operators, extending the Krein--Rutman theorem, and provides a more general version for commuting operators, advancing the theoretical understanding of operator eigenfunctionals.

Contribution

It presents a new eigenfunctional theorem for positive operators and generalizes it to commuting operators, enhancing the theoretical framework in operator theory.

Findings

Established an eigenfunctional theorem for positive operators

Extended the theorem to joint eigenfunctionals for commuting operators

Provides foundational results in operator theory

Abstract

We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.