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A characterization of Radon planes using generalized Day–James spaces

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Abstract

Radon planes are two-dimensional real normed spaces in which Birkhoff(-James) orthogonality is symmetic. It is shown that every Radon plane is isometrically isomorphic to a special Day–James space generated by a pair of an absolute norm and its dual norm.

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Acknowledgements

This work was supported in part by Grants-in-Aid for Scientific Research Grant Numbers 17K05287, 15K04920, Japan Society for the Promotion of Science.

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Author notes

  1. Naoto Komuro

    Present address: Department of Mathematics, Hokkaido University of Education, Asahikawa Campus, Asahikawa, 070-8621, Japan

Authors and Affiliations

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

    Kichi-Suke Saito

  2. Faculty of Industrial Science and Technology, Tokyo University of Science, Oshamanbe, Hokkaido, 049-3514, Japan

    Ryotaro Tanaka

Authors
  1. Naoto Komuro
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  2. Kichi-Suke Saito
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  3. Ryotaro Tanaka
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Corresponding author

Correspondence to Naoto Komuro.

Additional information

Communicated by Patrick N. Dowling.

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Komuro, N., Saito, KS. & Tanaka, R. A characterization of Radon planes using generalized Day–James spaces. Ann. Funct. Anal. 11, 62–74 (2020). https://doi.org/10.1007/s43034-019-00018-z

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  • DOI: https://doi.org/10.1007/s43034-019-00018-z

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