The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces

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发表日期：

2024年2月26日

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Yuankang Fu,
Huayou Xie,
Yongjin Li

摘要

In this paper, we shall consider a new constant $DW_B(X)$ $D W_{B} (X)$ which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant $DW^p_B(X)$ $D W_{B}^{p} (X)$ that is a generalization of $DW_B(X)$ $D W_{B} (X)$ . Interestingly, the upper bounds of $DW_B(X)$ $D W_{B} (X)$ and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of $DW^p_B(l_\infty -l_1)$ $D W_{B}^{p} (l_{\infty} - l_{1})$ .