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Dentability indices and locally uniformly convex renormings. (English) Zbl 0801.46010
Summary: We prove that if the dentability index \(\delta (X)\) of a Banach space \(X\) is less than \(\omega_ 1\) (first uncountable ordinal), then \(X\) admits an equivalent locally uniformly convex norm. We prove also that if its weak\(^*\) dentability index \(\delta^* (X)\) is less than \(\omega_ 1\), then \(X\) admits an equivalent norm whose dual norm is locally uniformly convex.

MSC:
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46B03 Isomorphic theory (including renorming) of Banach spaces
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