Study on Orthogonal Sets for Birkhoff Orthogonality

Xiaomei Wang, Donghai Ji () and Yueyue Wei
Additional contact information
Xiaomei Wang: Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Donghai Ji: Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Yueyue Wei: Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China

Mathematics, 2023, vol. 11, issue 20, 1-11

Abstract: We introduce the notion of orthogonal sets for Birkhoff orthogonality, which we will call Birkhoff orthogonal sets in this paper. As a generalization of orthogonal sets in Hilbert spaces, Birkhoff orthogonal sets are not necessarily linearly independent sets in finite-dimensional real normed spaces. We prove that the Birkhoff orthogonal set A = { x 1 , x 2 , … , x n } ( n ≥ 3 ) containing n − 3 right symmetric points is linearly independent in smooth normed spaces. In particular, we obtain similar results in strictly convex normed spaces when n = 3 and in both smooth and strictly convex normed spaces when n = 4 . These obtained results can be applied to the mutually Birkhoff orthogonal sets studied in recently.

Keywords: Birkhoff orthogonality; symmetry; orthogonal set; strictly convexity; smoothness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/20/4320/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/20/4320/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:20:p:4320-:d:1261431

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().