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<p>The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied, and three related geometric constants are introduced. New characterizations of inner product spaces are also presented. From the perspective of minimal width, strong <i>ε</i>-symmetry of Birkhoff orthogonality is introduced, and its relation to <i>ε</i>-symmetry of Birkhoff orthogonality is shown. Unlike most of the existing parameters of the underlying space, these new constants are full dimensional in nature.</p>

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Minimal widths and orthogonality types

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Chan He,
  • Horst Martini,
  • Senlin Wu

摘要

The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied, and three related geometric constants are introduced. New characterizations of inner product spaces are also presented. From the perspective of minimal width, strong ε-symmetry of Birkhoff orthogonality is introduced, and its relation to ε-symmetry of Birkhoff orthogonality is shown. Unlike most of the existing parameters of the underlying space, these new constants are full dimensional in nature.