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Abstract <p> We prove a noncommutative analog of the Radon–Nikodým theorem for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation>-tuples of completely positive mappings on Hilbert <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-modules covariant with respect to the action of a locally compact group. As an application, we describe the structure of the convex set of equivalence classes of completely positive tuples majorized by a given completely positive tuple. We also show that the classical Radon–Nikodým theorem follows from its noncommutative analog. </p>

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On a Class of Completely Positive Mappings

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. K. Gutnova

摘要

Abstract

We prove a noncommutative analog of the Radon–Nikodým theorem for \(n\) -tuples of completely positive mappings on Hilbert \(C^*\) -modules covariant with respect to the action of a locally compact group. As an application, we describe the structure of the convex set of equivalence classes of completely positive tuples majorized by a given completely positive tuple. We also show that the classical Radon–Nikodým theorem follows from its noncommutative analog.