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http://dx.doi.org/10.5666/KMJ.2022.62.2.271

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)
Publication Information
Kyungpook Mathematical Journal / v.62, no.2, 2022 , pp. 271-287 More about this Journal
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
Banach spaces; isosceles orthogonality; geometric constants; geometric properties;
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