Around Kutateladze’s Stratification Principle

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A linear functional on a real vector space is determined up to a scalar by its zero hyperplane. A linear operator is recovered from its kernel up to a simple multiplier in rather special cases. Nevertheless, some operator analog of the functional case is valid: 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 idea Kutateladze’s stratification principle. Two approaches are outlined: a standard approach, based on the concept of a local Hamel basis, and a nonstandard approach, involving Boolean valued analysis. It is clarified under what conditions the principle works. Some new applications to simultaneous inequalities with linear and multilinear operators are also given.