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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On characterizations of inner product spaces
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by Detlef Laugwitz PDF
Proc. Amer. Math. Soc. 50 (1975), 184-188 Request permission

Abstract:

The characterizations of inner product norms given by Tapia [10] make use of a generalized inner product in normed spaces. I shall give simpler proofs and a sharper result using a more geometrical approach.
References
  • Wilhelm Blaschke, Kreis und Kugel, Walter de Gruyter & Co., Berlin, 1956 (German). 2te Aufl. MR 0077958
  • T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Springer-Verlag, Berlin-New York, 1974 (German). Berichtigter Reprint. MR 0344997
  • Ludwig Danzer, Detlef Laugwitz, and Hanfried Lenz, Über das Löwnersche Ellipsoid und sein Analogon unter den einem Eikörper einbeschriebenen Ellipsoiden, Arch. Math. (Basel) 8 (1957), 214–219 (German). MR 94771, DOI 10.1007/BF01899996
  • Detlef Laugwitz, Differentialgeometrie in Vektorräumen, unter besonderer Berücksichtigung der unendlichdimensionalen Räume, Friedr. Vieweg & Sohn, Braunschweig, 1965 (German). MR 0182924
  • Detlef Laugwitz, Konvexe Mittelpunktsbereiche und normierte Räume, Math. Z. 61 (1954), 235–244 (German). MR 66667, DOI 10.1007/BF01181345
  • Detlef Laugwitz and Edgar R. Lorch, Riemann metrics associated with convex bodies and normed spaces, Amer. J. Math. 78 (1956), 889–894. MR 82081, DOI 10.2307/2372473
  • E. R. Lorch, A curvature study of convex bodies in Banach spaces, Ann. Mat. Pura Appl. (4) 34 (1953), 105–112. MR 52679, DOI 10.1007/BF02415327
    • J. Radon, Über eine besondere Art ebener konvexer Kurven, Leipziger Ber. Math.-Phys. Kl. 68 (1916), 123-128.
  • Hanno Rund, The differential geometry of Finsler spaces, Die Grundlehren der mathematischen Wissenschaften, Band 101, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959. MR 0105726
    • R. A. Tapia, A characterization of inner product spaces, Bull. Amer. Math. Soc. 79 (1973), 530-531; MR 47 #3964. Extended version, Proc. Amer. Math. Soc. 41 (1973), 569-574.
  • Frederick A. Valentine, Konvexe Mengen, B. I. Hochschultaschenbücher, Band 402/402a, Bibliographisches Institut, Mannheim, 1968 (German). Übersetzung aus dem Englischen durch E. Heil. MR 0226495
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 50 (1975), 184-188
  • MSC: Primary 46B05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0374873-0
  • MathSciNet review: 0374873