Paper Title:

Two Geometric Constants Related to Isosceles Orthogonality on Banach Space

Author(s):

Huayou Xie, Qi Liu and Yongjin Li

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: xiehy33@mail2.sysu.edu.cn

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: liuq325@mail2.sysu.edu.cn

Department of Mathematics,
Sun Yat-sen University,
 Guangzhou, 510275,
P. R. China.
E-mail: stslyj@mail.sysu.edu.cn

Abstract:

In this paper, we introduce new geometric constant C(X,a_i,b_i,c_i,2) to measure the difference between isosceles orthogonality and special Carlsson orthogonalities. At the same time, we also present the geometric constant C(X,a_i,b_i,c_i), which is a generalization of the rectangular constant proposed by Joly. According to the inequality on isosceles orthogonality, we give the boundary characterization of these geometric constants. Then the relationship between these geometric constants and uniformly non-square property can also be discussed. Furthermore, we show that there is a close relationship between these geometric constants and some important geometric constants.

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