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Does there exists a strictly convex Banach space which is not uniformly convex and has normal structure ?

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  • $\begingroup$ You may consider accepting my answer. $\endgroup$ – Tomasz Kania Sep 7 '14 at 14:31
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Yes. This is Theorem 3.1 in

L. P. Belluce, W. A. Kirk, and E. F. Steiner, Normal structure in Banach spaces. Pacific J. Math. 6, (1968), 433-440.

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