Some results on the Dunkl-Williams constant
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917387422400512 |
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| author | Alonso, Javier Martín, Pedro |
| author_facet | Alonso, Javier Martín, Pedro |
| contents | This paper presents a compilation of various formulas for calculating the Dunkl-Williams constant $DW(X)$ of a real normed linear space. The constant $DW_B(X)$ related to Birkhoff orthogonality is also considered. The value of $DW(X)$ is calculated for several two-dimensional spaces. In particular, it is shown that the Dunk-Williams constant for $\ell_2-\ell_1$ is equal to $2\sqrt{2}$, and that it is equal to $8(2-\sqrt3)$ for the two dimensional normed linear space whose unit sphere is a dodecahedron. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02918 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some results on the Dunkl-Williams constant Alonso, Javier Martín, Pedro Functional Analysis 46B20 This paper presents a compilation of various formulas for calculating the Dunkl-Williams constant $DW(X)$ of a real normed linear space. The constant $DW_B(X)$ related to Birkhoff orthogonality is also considered. The value of $DW(X)$ is calculated for several two-dimensional spaces. In particular, it is shown that the Dunk-Williams constant for $\ell_2-\ell_1$ is equal to $2\sqrt{2}$, and that it is equal to $8(2-\sqrt3)$ for the two dimensional normed linear space whose unit sphere is a dodecahedron. |
| title | Some results on the Dunkl-Williams constant |
| topic | Functional Analysis 46B20 |
| url | https://arxiv.org/abs/2604.02918 |