A weighted Birkhoff orthogonal James-type constant
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914620736798720 |
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| author | Qi, Junxiang Yin, Zhouping Liu, Qi Li, Yongjin |
| author_facet | Qi, Junxiang Yin, Zhouping Liu, Qi Li, Yongjin |
| contents | Let $X$ be a real Banach space and $λ\in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_λ^{\perp}(X)=\sup \left\{\min \{\|λx+(1-λ) y\|,\|λx-(1-λ) y\|\}: x, y \in S_X, x \perp_B y\right\},$$ where \(λ\in[0,1]\) and $x \perp_B y$ stands for Birkhoff orthogonality. We establish its basic bounds, stability properties, and reduction principles, and clarify its relations with the orthogonal James constant $J_{\perp}(X)$. The 2 -Lipschitz continuity of $J_λ^{\perp}(X)$ with respect to $λ$ is proved. New characterizations of uniformly nonsquare spaces are obtained; in particular, $J_λ^{\perp}(X)=1$ for some $λ\in(0,1)$ if and only if $X$ is not uniformly nonsquare. We also discuss connections with strict convexity, uniform convexity, modulus of smoothness, and the von Neumann-Jordan constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A weighted Birkhoff orthogonal James-type constant Qi, Junxiang Yin, Zhouping Liu, Qi Li, Yongjin Functional Analysis 46B20 Let $X$ be a real Banach space and $λ\in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_λ^{\perp}(X)=\sup \left\{\min \{\|λx+(1-λ) y\|,\|λx-(1-λ) y\|\}: x, y \in S_X, x \perp_B y\right\},$$ where \(λ\in[0,1]\) and $x \perp_B y$ stands for Birkhoff orthogonality. We establish its basic bounds, stability properties, and reduction principles, and clarify its relations with the orthogonal James constant $J_{\perp}(X)$. The 2 -Lipschitz continuity of $J_λ^{\perp}(X)$ with respect to $λ$ is proved. New characterizations of uniformly nonsquare spaces are obtained; in particular, $J_λ^{\perp}(X)=1$ for some $λ\in(0,1)$ if and only if $X$ is not uniformly nonsquare. We also discuss connections with strict convexity, uniform convexity, modulus of smoothness, and the von Neumann-Jordan constant. |
| title | A weighted Birkhoff orthogonal James-type constant |
| topic | Functional Analysis 46B20 |
| url | https://arxiv.org/abs/2606.01068 |