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A new type of orthogonality for normed planes

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Abstract

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d ⩾ 3.

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Authors and Affiliations

  1. Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany

    Horst Martini & Margarita Spirova

Authors
  1. Horst Martini
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  2. Margarita Spirova
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Research supported by Deutsche Forschungsgemeinschaft.

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Martini, H., Spirova, M. A new type of orthogonality for normed planes. Czech Math J 60, 339–349 (2010). https://doi.org/10.1007/s10587-010-0039-x

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  • DOI: https://doi.org/10.1007/s10587-010-0039-x

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