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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19295 |
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| _version_ | 1866910234963869696 |
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| author | Hieu, Doan Huu Cuong, Nguyen Duy |
| author_facet | Hieu, Doan Huu Cuong, Nguyen Duy |
| contents | The paper studies a generalized von Neumann-Jordan constant of non-normable metrics on vector spaces. To the best of our knowledge, all existing results of the von Neumann-Jordan constant and its generalizations have been established only in the normed setting. We identify reasonable conditions on non-normable metrics under which results known for norms remain valid. Several examples and counterexamples are provided to justify the established results. The computation for a class of non-normable metrics on product spaces is also investigated. In particular, we give precise formulas for the generalized von Neumann-Jordan constant of p-metrics under a metric-type Clarkson inequality. Comparisons with existing results are discussed throughout the paper whenever applicable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19295 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A von Neumann-Jordan Constant of Non-Normable Metrics Hieu, Doan Huu Cuong, Nguyen Duy Functional Analysis 46B20, 46B25, 46C15, 46C50, 52A41 The paper studies a generalized von Neumann-Jordan constant of non-normable metrics on vector spaces. To the best of our knowledge, all existing results of the von Neumann-Jordan constant and its generalizations have been established only in the normed setting. We identify reasonable conditions on non-normable metrics under which results known for norms remain valid. Several examples and counterexamples are provided to justify the established results. The computation for a class of non-normable metrics on product spaces is also investigated. In particular, we give precise formulas for the generalized von Neumann-Jordan constant of p-metrics under a metric-type Clarkson inequality. Comparisons with existing results are discussed throughout the paper whenever applicable. |
| title | A von Neumann-Jordan Constant of Non-Normable Metrics |
| topic | Functional Analysis 46B20, 46B25, 46C15, 46C50, 52A41 |
| url | https://arxiv.org/abs/2605.19295 |