Affiliation:
1. Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
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={x1,x2,…,xn}(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.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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