Primal and dual characterizations of sign-symmetric norms
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911627332288512 |
|---|---|
| author | Cuong, Nguyen Duy |
| author_facet | Cuong, Nguyen Duy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19642 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Primal and dual characterizations of sign-symmetric norms Cuong, Nguyen Duy Functional Analysis 49J52, 49J53, 49K40, 90C30, 90C46 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. |
| title | Primal and dual characterizations of sign-symmetric norms |
| topic | Functional Analysis 49J52, 49J53, 49K40, 90C30, 90C46 |
| url | https://arxiv.org/abs/2504.19642 |