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Proceedings of the American Mathematical Society

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

 

 

Banach spaces that have normal structure and are isomorphic to a Hilbert space


Authors: Javier Bernal and Francis Sullivan
Journal: Proc. Amer. Math. Soc. 90 (1984), 550-554
MSC: Primary 46B20; Secondary 46C05
MathSciNet review: 733404
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Abstract: We prove that given a Hilbert space $ \left( {E,\vert\vert \cdot \vert\vert} \right)$, and $ \vert \cdot \vert$ a norm on $ E$ such that for all $ x \in E$, $ 1/\beta \left\vert x \right\vert \leqslant \left\Vert x \right\Vert \leqslant \left\vert x \right\vert$ for some $ \beta $, if $ 1 \leqslant \beta < \sqrt 2 $, then $ \left( {E,\vert \cdot \vert} \right)$ satisfies a convexity property from which normal structure follows.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0733404-9
Article copyright: © Copyright 1984 American Mathematical Society