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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}
}