How orthogonality influences geometric constants
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914001543233536 |
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| author | Wang, Yuxin Liu, Qi Bao, Mengmeng |
| author_facet | Wang, Yuxin Liu, Qi Bao, Mengmeng |
| contents | In this paper, based on isosceles orthogonality, we have found equivalent definitions for four constants: $A_2(X)$ proposed by Baronti in 2000 [J. Math. Anal. Appl. 252(2000), 124-146], $C'_{\mathrm{NJ}}(X)$ introduced by Alonso et al. in 2008 [Stud. Math. 188(2008), 135-150], $T(X)$ introduced by Alonso et al. in 2008 [J. Math. Anal. Appl. 340(2008), 1271-1283] and $L'_{\mathrm{YJ}}(X)$ put forward by Liu et al. in 2022 [Bull. Malays. Math. Sci. Soc., 45(2022),307-321]. A core commonality among these three constants is that they are all restricted to the unit sphere. This finding provides us with an insight: could it be that several constants defined over the entire space, when combined with orthogonality conditions, are equivalent to being restricted to the unit sphere? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How orthogonality influences geometric constants Wang, Yuxin Liu, Qi Bao, Mengmeng Functional Analysis In this paper, based on isosceles orthogonality, we have found equivalent definitions for four constants: $A_2(X)$ proposed by Baronti in 2000 [J. Math. Anal. Appl. 252(2000), 124-146], $C'_{\mathrm{NJ}}(X)$ introduced by Alonso et al. in 2008 [Stud. Math. 188(2008), 135-150], $T(X)$ introduced by Alonso et al. in 2008 [J. Math. Anal. Appl. 340(2008), 1271-1283] and $L'_{\mathrm{YJ}}(X)$ put forward by Liu et al. in 2022 [Bull. Malays. Math. Sci. Soc., 45(2022),307-321]. A core commonality among these three constants is that they are all restricted to the unit sphere. This finding provides us with an insight: could it be that several constants defined over the entire space, when combined with orthogonality conditions, are equivalent to being restricted to the unit sphere? |
| title | How orthogonality influences geometric constants |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2507.17122 |