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arXiv · 2504.19642

Primal and dual characterizations of sign-symmetric norms

Nguyen Duy Cuong
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Abstract

The paper studies primal and dual characterizations of a class of sign-symmetric norms on product vector spaces. Correspondences between these norms and a class of convex functions are established. Explicit formulas for the dual norm and the convex subdifferential of a given primal norm are derived. It is demonstrated that this class of norms is well-suited for studying properties and problems on product spaces. As an application, we study the von Neumann-Jordan constant of norms on product spaces and extend a classical result of Clarkson from Lebesgue spaces to general normed vector spaces.

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BibTeXRIS

Nguyen Duy Cuong. 2025-04-28. Primal and dual characterizations of sign-symmetric norms. https://doi.org/10.1007/s11117-026-01193-9

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