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<p>We study invariant subsets of a certain family of nonlinear operators acting on the set of&#xa0;Banach limits.We provide conditions under which an operator from this family coincides with the&#xa0;identity operator.We establish new properties of the extreme points of the set of Banach limits, which indicate their certain mutual independence.</p>

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Operators Defined on the Set of Banach Limits

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • S. V. Astashkin,
  • E. M. Semenov,
  • A. S. Usachev

摘要

We study invariant subsets of a certain family of nonlinear operators acting on the set of Banach limits.We provide conditions under which an operator from this family coincides with the identity operator.We establish new properties of the extreme points of the set of Banach limits, which indicate their certain mutual independence.