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

Bernal, Javier; Sullivan, Francis

doi:10.1090/S0002-9939-1984-0733404-9

Banach spaces that have normal structure and are isomorphic to a Hilbert space
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by Javier Bernal and Francis Sullivan

Proc. Amer. Math. Soc. 90 (1984), 550-554

DOI: https://doi.org/10.1090/S0002-9939-1984-0733404-9

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Abstract:

We prove that given a Hilbert space $\left ( {E,|| \cdot ||} \right )$, and $| \cdot |$ a norm on $E$ such that for all $x \in E$, $1/\beta \left | x \right | \leqslant \left \| x \right \| \leqslant \left | x \right |$ for some $\beta$, if $1 \leqslant \beta < \sqrt 2$, then $\left ( {E,| \cdot |} \right )$ satisfies a convexity property from which normal structure follows.

References

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Behavior of

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