Dual of extremal absolute norms on R2 and the James constant

Masahiro Sato; Naoto Komuro; Ken-Ichi Mitani; Kichi-Suke Saito; Ryotaro Tanaka

doi:10.1215/17358787-3492677

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Home > Journals > Banach J. Math. Anal. > Volume 10 > Issue 2 > Article

April 2016 Dual of extremal absolute norms on

\mathbb{R}^{2}

and the James constant

Masahiro Sato, Naoto Komuro, Ken-Ichi Mitani, Kichi-Suke Saito, Ryotaro Tanaka

Banach J. Math. Anal. 10(2): 251-266 (April 2016). DOI: 10.1215/17358787-3492677

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Abstract

The set of all absolute normalized norms on $\mathbb{R}^{2}$ (denoted by $AN_{2}$ ) has a convex structure with respect to the usual operation. In a previous article, N. Komuro, K.-S. Saito, and K.-I. Mitani calculated the James constants of $(\mathbb{R}^{2},\Vert \cdot\Vert )$ when $\Vert \cdot\Vert$ is an extreme point of $AN_{2}$ . In this article, we calculate the James constant of its dual space.

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Masahiro Sato. Naoto Komuro. Ken-Ichi Mitani. Kichi-Suke Saito. Ryotaro Tanaka. "Dual of extremal absolute norms on $\mathbb{R}^{2}$ and the James constant." Banach J. Math. Anal. 10 (2) 251 - 266, April 2016. https://doi.org/10.1215/17358787-3492677