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arXiv · 2602.13974

Generalized geometric constants related to Birkhoff orthogonality in Banach spaces

Junxiang Qi·Qian Li·Zhouping Yin·Qi Liu·Jiaye Bi·Yuankang Fu·Yongjin Li
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Abstract

In this paper, based on Birkhoff orthogonality, we introduce two geometric constants $\boldsymbol{A}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ and $\boldsymbol{D}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ in Banach spaces, which generalize the skew geometric constants related to Birkhoff orthogonality. We systematically investigate the basic properties of the two constants, including their upper and lower bounds, and establish the equivalent characterizations for Banach spaces being uniformly non-square. Additionally, we explore the relationship between $\boldsymbol{D}_{\boldsymbol{t}}^{\boldsymbol{B}}(\boldsymbol{X})$ and the modulus of convexity $\boldsymbol{\delta}_{\boldsymbol{X}}(\boldsymbol{\varepsilon})$. Finally, we explore several applications of the two newly proposed geometric constants.

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Junxiang Qi, Qian Li, Zhouping Yin, Qi Liu, Jiaye Bi, Yuankang Fu, Yongjin Li. 2026-02-15. Generalized geometric constants related to Birkhoff orthogonality in Banach spaces. https://arxiv.org/abs/2602.13974

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