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Inspheres and inner products

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Abstract

Among normed linear spacesX of dimension ≧3, finite-dimensional Hilbert spaces are characterized by the condition that for each convex bodyC inX and each ballB of maximum radius contained inC,B’s center is a convex combination of points ofB ∩ (boundary ofC). Among reflexive Banach spaces of dimension ≧3, general Hilbert spaces are characterized by a related but weaker condition on inscribed balls.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, Washington, USA

    Victor Klee

  2. Dipartimento di Matematica, Università degli Studi, Via Saldini 50, 20133, Milano, Italy

    Elisabetta Maluta & Clemente Zanco

Authors
  1. Victor Klee
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  2. Elisabetta Maluta
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  3. Clemente Zanco
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Additional information

Research of the first author was partially supported by the U.S. National Science Foundation. Research of the second and third authors was supported by the Consiglio Nazionale delle Ricerche and the Ministero della Pubblica Istruzione of Italy, while they were visiting the University of Washington, Seattle, USA.

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Klee, V., Maluta, E. & Zanco, C. Inspheres and inner products. Israel J. Math. 55, 1–14 (1986). https://doi.org/10.1007/BF02772692

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  • DOI: https://doi.org/10.1007/BF02772692

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