Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces

Emelyanov, Eduard; Erkurşun Özcan, NAZİFE; Gorokhova, Svetlana

doi:10.1007/s00025-025-02386-6

Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces

Emelyanov E., Erkurşun Özcan N., Gorokhova S.

RESULTS IN MATHEMATICS, vol.80, pp.1-14, 2025 (SCI-Expanded, Scopus)

Publication Type: Article / Article
Volume: 80
Publication Date: 2025
Doi Number: 10.1007/s00025-025-02386-6
Journal Name: RESULTS IN MATHEMATICS
Journal Indexes: Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
Page Numbers: pp.1-14
Open Archive Collection: AVESIS Open Access Collection
Hacettepe University Affiliated: Yes

Abstract

It is proved that: each collectively order continuous set of operators from an Archimedean ordered vector space with a generating cone to an ordered vector space 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.