Geometric constants of π/2-rotation invariant norms on R2

Yukino Tomizawa; Ken-Ichi Mitani; Kichi-Suke Saito; Ryotaro Tanaka

doi:10.1215/20088752-0000007X

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Home > Journals > Ann. Funct. Anal. > Volume 8 > Issue 2 > Article

May 2017 Geometric constants of

\pi/2

-rotation invariant norms on

\mathbb{R}^{2}

Yukino Tomizawa, Ken-Ichi Mitani, Kichi-Suke Saito, Ryotaro Tanaka

Ann. Funct. Anal. 8(2): 215-230 (May 2017). DOI: 10.1215/20088752-0000007X

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Abstract

In this article, we study the (modified) von Neumann–Jordan constant and Zbăganu constant of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ . Some estimations of these geometric constants are given. As an application, we construct various examples consisting of $\pi/2$ -rotation invariant norms.

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Yukino Tomizawa. Ken-Ichi Mitani. Kichi-Suke Saito. Ryotaro Tanaka. "Geometric constants of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ ." Ann. Funct. Anal. 8 (2) 215 - 230, May 2017. https://doi.org/10.1215/20088752-0000007X