A short proof of the Arendt-Chernoff-Kato theorem

TL;DR

This paper presents a concise new proof of the Arendt-Chernoff-Kato theorem, simplifying the characterization of generators of positive semigroups in order unit spaces by avoiding complex mathematical tools.

Contribution

It introduces a novel proof technique that bypasses half-norms and subdifferentials, offering a simpler approach even for matrix cases.

Findings

Provides a shorter, more accessible proof of the theorem.

Introduces a new sufficient condition for operators to have positive inverses.

Enhances understanding of positive semigroup generators in order unit spaces.

Abstract

We give a short new proof of the Arendt-Chernoff-Kato theorem, which characterizes generators of positive C0 semigroups in order unit spaces. The proof avoids half-norms and subdifferentials, and is based on a sufficient condition for an operator to have positive inverse, which is new even for matrices.