Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A New Geometric Constant in Banach Spaces Related to the Isosceles Orthogonality

  • Yang, Zhijian (Department of Mathematics, Sun Yat-sen University) ;
  • Li, Yongjin (Department of Mathematics, Sun Yat-sen University)
  • Received : 2022.02.25
  • Accepted : 2022.04.18
  • Published : 2022.06.30
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Abstract

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogonal geometric constant ΩX(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogonal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of ΩX(α) and γX(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric properties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of P. R. China (Nos. 11971493 and 12071491).

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