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<p>A linear functional on a real vector space is determined up to a scalar by its zerohyperplane. A linear operator is recovered from its kernel up to a simple multiplierin rather special cases. Nevertheless, some operator analog of the functional case isvalid: each operator with target a&#xa0;Kantorovich space, a&#xa0;Dedekind complete vector lattice,is determined up to some orthomorphism by the kernels of its strata. We call this ideaKutateladze’s stratification principle. Two approaches are outlined: a&#xa0;standardapproach, based on the concept of a&#xa0;local Hamel basis, and a&#xa0;nonstandard approach, involvingBoolean valued analysis. It is clarified under what conditions the principleworks. Some new applications to simultaneous inequalities with linear and multilinearoperators are also given.</p>

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Around Kutateladze’s Stratification Principle

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • A. G. Kusraev

摘要

A linear functional on a real vector space is determined up to a scalar by its zerohyperplane. A linear operator is recovered from its kernel up to a simple multiplierin rather special cases. Nevertheless, some operator analog of the functional case isvalid: each operator with target a Kantorovich space, a Dedekind complete vector lattice,is determined up to some orthomorphism by the kernels of its strata. We call this ideaKutateladze’s stratification principle. Two approaches are outlined: a standardapproach, based on the concept of a local Hamel basis, and a nonstandard approach, involvingBoolean valued analysis. It is clarified under what conditions the principleworks. Some new applications to simultaneous inequalities with linear and multilinearoperators are also given.