Generalized geometric constants related to Birkhoff orthogonality in Banach spaces
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866908839000932352 |
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| author | Qi, Junxiang Li, Qian Yin, Zhouping Liu, Qi Bi, Jiaye Fu, Yuankang Li, Yongjin |
| author_facet | Qi, Junxiang Li, Qian Yin, Zhouping Liu, Qi Bi, Jiaye Fu, Yuankang Li, Yongjin |
| contents | 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 $\boldsymbolδ_{\boldsymbol{X}}(\boldsymbol{\varepsilon})$. Finally, we explore several applications of the two newly proposed geometric constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13974 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized geometric constants related to Birkhoff orthogonality in Banach spaces Qi, Junxiang Li, Qian Yin, Zhouping Liu, Qi Bi, Jiaye Fu, Yuankang Li, Yongjin Functional Analysis 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 $\boldsymbolδ_{\boldsymbol{X}}(\boldsymbol{\varepsilon})$. Finally, we explore several applications of the two newly proposed geometric constants. |
| title | Generalized geometric constants related to Birkhoff orthogonality in Banach spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.13974 |