New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls

Symmetry

Qi Liu¹  Yuankang Fu¹  Yongjin Li¹ 

[1] School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China;

关键词: Banach space;    geometric constant;    normal structure;    uniformly non-square;    uniformly convex;   

DOI  :  10.3390/sym13060951

来源: DOAJ

【 摘 要 】

Geometric constant is one of the important tools to study geometric properties of Banach spaces. In this paper, we will introduce two new geometric constants $J_L\left(X\right)$ and $Y_J\left(X\right)$ in Banach spaces, which are symmetric and related to the side lengths of inscribed equilateral triangles of unit balls. The upper and lower bounds of $J_L\left(X\right)$ and $Y_J\left(X\right)$ as well as the values of $J_L\left(X\right)$ and $Y_J\left(X\right)$ for Hilbert spaces and some common Banach spaces will be calculated. In addition, some inequalities for $J_L\left(X\right)$, $Y_J\left(X\right)$ and some significant geometric constants will be presented. Furthermore, the sufficient conditions for uniformly non-square and normal structure, and the necessary conditions for uniformly non-square and uniformly convex will be established.

【 授权许可】

Unknown