Open Journal of Mathematical Sciences
Vol. 7 (2023), Issue 1, pp. 1-7
ISSN: 2523-0212 (Online) 2616-4906 (Print)
DOI: 10.30538/oms2024.0219
The skew constant and orthogonalities in Banach spaces
Yin Zhou\(^{1}\) , Qichuan Ni\(^{1,*}\) , Qi Liu\(^{1}\)
\(^{1}\) School of Mathematics and Physics, Anqing Normal University, Anqing 246133, P. R. China; niqichuan111@163.com.
Copyright © 2024 Yin Zhou, Qichuan Ni and Qi Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: August 18, 2023 – Accepted: February 12, 2024 – Published: May 15, 2024
Abstract
In normed spaces, Birkhoff orthogonality and isosceles orthogonality can be used to characterize space structures, and many scholars have introduced geometric constants to quantitatively describe the relationship between these two types of orthogonality. This paper introduces a new orthogonal relationship – Skew orthogonality – and proposes a new geometric constant to measure the “distance” of difference between skew orthogonality and Birkhoff orthogonality in normed spaces. In the end, we provide some examples of specific spaces.
Keywords:
Birkhoff orthogonality; geometric constant; Hilbert spaces; uniformly non-square