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2016 The constants related to isosceles orthogonality in normed spaces and its dual
Hiroyasu Mizuguchi
Nihonkai Math. J. 27(1-2): 41-58 (2016).

Abstract

We consider isosceles orthogonality and Birkhoff orthogonality, which are the most used notions of generalized orthogonality. In 2006, Ji and Wu introduced a geometric constant $D(X)$ to give a quantitative characterization of the difference between these two orthogonality types. From their results, we have that $D(X)=D(X^*)$ holds for any symmetric Minkowski plane. On the other hand, for the James constant $J(X)$, Saito, Sato and Tanaka recently showed that if the norm of a two-dimensional space $X$ is absolute and symmetric then $J(X)=J(X^*)$ holds. In this paper, we consider the constant $D(X,\lambda)$ such that $D(X)=\inf_{\lambda \in \mathbb{R}}D(X,\lambda)$ and obtain that in the same situation $D(X,\lambda)=D(X^*,\lambda)$ holds for any $\lambda \in (0,1)$.

Citation

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Hiroyasu Mizuguchi. "The constants related to isosceles orthogonality in normed spaces and its dual." Nihonkai Math. J. 27 (1-2) 41 - 58, 2016.

Information

Received: 16 December 2015; Revised: 25 April 2016; Published: 2016
First available in Project Euclid: 14 September 2017

zbMATH: 1381.46015
MathSciNet: MR3698240

Subjects:
Primary: 46B20

Keywords: ‎absolute normalized norm , Birkhoff orthogonality , isosceles orthogonality , piecewise linear function

Rights: Copyright © 2016 Niigata University, Department of Mathematics

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Vol.27 • No. 1-2 • 2016
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