Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces

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

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

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