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Rotund complex normed linear spaces


Authors: P. R. Beesack, E. Hughes and M. Ortel
Journal: Proc. Amer. Math. Soc. 75 (1979), 42-44
MSC: Primary 46B20
DOI: https://doi.org/10.1090/S0002-9939-1979-0529209-2
MathSciNet review: 529209
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Abstract: We show that rotundity in a complex normed linear space is equivalent to the property that for any distinct vectors x and y of unit norm, a complex number $ \alpha $ may be found for which $ \left\Vert {\alpha x + (1 - \alpha )y} \right\Vert < 1$. This leads to a natural proof of a result due to Taylor and Foguel on the uniqueness of Hahn-Banach extensions.


References [Enhancements On Off] (What's this?)

  • [1] A. E. Taylor, The extension of linear functionals, Duke Math J. 5 (1939), 538-547. MR 1, p. 58. MR 0000345 (1:58b)
  • [2] S. R. Foguel, On a theorem by A. E. Taylor, Proc. Amer. Math. Soc. 9 (1958), 325. MR 20 #219. MR 0093696 (20:219)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0529209-2
Keywords: Rotund, strictly convex, Hahn-Banach extensions
Article copyright: © Copyright 1979 American Mathematical Society

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