Collective order boundedness of sets of operators between ordered vector spaces
Functional Analysis
2025-02-04 v4
Abstract
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given.
Keywords
Cite
@article{arxiv.2410.17030,
title = {Collective order boundedness of sets of operators between ordered vector spaces},
author = {Eduard Emelyanov and Nazife Erkursun-Ozcan and Svetlana Gorokhova},
journal= {arXiv preprint arXiv:2410.17030},
year = {2025}
}