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A Comparison Between James and von Neumann–Jordan Constants

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Abstract

In this paper, we compare James and von Neumann–Jordan constants of normed spaces under certain conditions. It is shown that if a normed space with James constant \(\sqrt{2}\) is three- or more dimensional, or is a \(\pi /2\)-rotation-invariant two-dimensional space, then its von Neumann–Jordan constant is less than or equal to \(4-2\sqrt{2}\).

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Author notes

  1. Yukino Tomizawa

    Present address: Department of Engineering, Faculty of Engineering, Niigata Institute of Technology, Niigata, 945-1195, Japan

Authors and Affiliations

  1. Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, Asahikawa, 070-8621, Japan

    Naoto Komuro

  2. Department of Information and Communication Engineering Faculty of Computer Science and System Engineering, Okayama Prefectural University, Okayama, 719-1197, Japan

    Ken-Ichi Mitani

  3. Department of Mathematical Sciences, Institute of Science and Technology, Niigata University, Niigata, 950-2181, Japan

    Kichi-Suke Saito

  4. Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Ryotaro Tanaka

  5. Department of Mathematics, Faculty of Science and Engineering, Chuo University, Tokyo, 112-8551, Japan

    Yukino Tomizawa

Authors
  1. Naoto Komuro
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  2. Ken-Ichi Mitani
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  3. Kichi-Suke Saito
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  4. Ryotaro Tanaka
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  5. Yukino Tomizawa
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Corresponding author

Correspondence to Ryotaro Tanaka.

Additional information

This work was supported in part by Grants-in-Aid for Scientific Research Grant Numbers 15K04920, 16J01162, Japan Society for the Promotion of Science, respectively.

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Komuro, N., Mitani, KI., Saito, KS. et al. A Comparison Between James and von Neumann–Jordan Constants. Mediterr. J. Math. 14, 168 (2017). https://doi.org/10.1007/s00009-017-0968-9

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  • DOI: https://doi.org/10.1007/s00009-017-0968-9

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