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Some results on the Dunkl-Williams constant

Javier Alonso, Pedro Martín

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.

Some results on the Dunkl-Williams constant

Abstract

This paper presents a compilation of various formulas for calculating the Dunkl-Williams constant of a real normed linear space. The constant related to Birkhoff orthogonality is also considered. The value of is calculated for several two-dimensional spaces. In particular, it is shown that the Dunk-Williams constant for is equal to , and that it is equal to for the two dimensional normed linear space whose unit sphere is a dodecahedron.

Paper Structure

This paper contains 1 section, 5 theorems, 180 equations.

Table of Contents

  1. Some examples

Key Result

Proposition 1

Let $X$ be a real normed linear space, and let us consider Then, $DW(X)=DW_i(X)$, $i=1,\ldots, 5$. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (15)

  • Proposition 1
  • proof
  • Proposition 2
  • Proposition 3
  • proof
  • Example 1
  • Example 2
  • Lemma 1
  • proof
  • Lemma 2
  • ...and 5 more