Rotund complex normed linear spaces
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- by P. R. Beesack, E. Hughes and M. Ortel PDF
- Proc. Amer. Math. Soc. 75 (1979), 42-44 Request permission
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 $\left \| {\alpha x + (1 - \alpha )y} \right \| < 1$. This leads to a natural proof of a result due to Taylor and Foguel on the uniqueness of Hahn-Banach extensions.References
- A. E. Taylor, The extension of linear functionals, Duke Math. J. 5 (1939), 538–547. MR 345
- Shaul R. Foguel, On a theorem by A. E. Taylor, Proc. Amer. Math. Soc. 9 (1958), 325. MR 93696, DOI 10.1090/S0002-9939-1958-0093696-3
Additional Information
- © Copyright 1979 American Mathematical Society
- 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