Proceedings of the American Mathematical Society

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

 

 

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
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.


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