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arXiv · 2604.02918

Some results on the Dunkl-Williams constant

Javier Alonso·Pedro Martín
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Abstract

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.

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Javier Alonso, Pedro Martín. 2026-04-03. Some results on the Dunkl-Williams constant. https://arxiv.org/abs/2604.02918

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