Dissipativity and positive off-diagonal property of operators on ordered Banach spaces

TL;DR

This paper investigates the relationship between $p$-contractivity and $p$-dissipativity of positive semigroups on ordered Banach spaces, introducing a sublinear function based on the space's order structure.

Contribution

It introduces a new sublinear function $p$ tailored to ordered Banach spaces and explores its role in the properties of positive semigroups and their generators.

Findings

Established a connection between $p$-contractivity and $p$-dissipativity.

Analyzed the positive off-diagonal property of generators.

Provided new insights into operator behavior on ordered Banach spaces.

Abstract

In this paper, we provide a sublinear function $p$ on ordered Banach spaces, which depends on the order structure of the space. With respect to this $p$, we study the relation between $p$-contractivity of positive semigroups and the $p$-dissipativity of its generators. The positive off-diagonal property of generators is also studied in ordered vector spaces.