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<p>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.</p>

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Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月15日

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  • Eduard Emelyanov,
  • Nazife Erkurşun-Özcan,
  • Svetlana Gorokhova

摘要

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.