The skew generalized Von Neumann Jordan constant in the unit sphere
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912120444026880 |
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| author | Wang, Yuxin Liu, Qi Xia, Jinyu Huang, Shuaizhe |
| author_facet | Wang, Yuxin Liu, Qi Xia, Jinyu Huang, Shuaizhe |
| contents | In this paper, we introduce a new constant for Banach spaces, denoted as $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$. We provide calculations for both the lower and upper bounds of this constant, as well as its exact values in certain Banach spaces. Furthermore, we give the inequality relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant and the other two constants. Besides, we establish an equivalent relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant and the $\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)$ constant. Specifically, we shall exhibit the connections between the constant $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ and certain geometric characteristics of Ba nach spaces, including uniform convexity and uniform nonsquareness. Additionally, a sufficient condition for uniform normal structure about the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant is also established. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_10094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The skew generalized Von Neumann Jordan constant in the unit sphere Wang, Yuxin Liu, Qi Xia, Jinyu Huang, Shuaizhe Functional Analysis 46B20, 46C15 F.2.2; I.2.7 In this paper, we introduce a new constant for Banach spaces, denoted as $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$. We provide calculations for both the lower and upper bounds of this constant, as well as its exact values in certain Banach spaces. Furthermore, we give the inequality relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant and the other two constants. Besides, we establish an equivalent relationship between the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant and the $\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)$ constant. Specifically, we shall exhibit the connections between the constant $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ and certain geometric characteristics of Ba nach spaces, including uniform convexity and uniform nonsquareness. Additionally, a sufficient condition for uniform normal structure about the $\widetilde{C}_{\mathrm{NJ}}^p(ξ, v, X)$ constant is also established. |
| title | The skew generalized Von Neumann Jordan constant in the unit sphere |
| topic | Functional Analysis 46B20, 46C15 F.2.2; I.2.7 |
| url | https://arxiv.org/abs/2411.10094 |