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arXiv · 2410.17030

Collective order boundedness of sets of operators between ordered vector spaces

Eduard Emelyanov·Nazife Erkursun-Ozcan·Svetlana Gorokhova
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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.

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Eduard Emelyanov, Nazife Erkursun-Ozcan, Svetlana Gorokhova. 2024-10-22. Collective order boundedness of sets of operators between ordered vector spaces. https://arxiv.org/abs/2410.17030

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