An operator theoretic approach to uniform (anti-)maximum principles

Maximum principles and uniform anti-maximum are a ubiquitous topic in PDE theory that is closely tied to the Krein--Rutman theorem kernel estimates for resolvents. We take up classical idea of Tak\'a\v{c} - prove (anti-)maximum an abstract operator theoretic framework combine it with recent ideas from eventually positive semigroups. This enables us derive necessary sufficient conditions very general setting. Consequently, we able either or disprove large variety concrete differential operators. As bonus, several operators already known satisfy not principles, our gives clear concise explanation this behaviour.