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Smoothness, asymptotic smoothness and the Blum-Hanson property

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Abstract

We isolate various sufficient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of asymptotic smoothness of X has an extremal behaviour at infinity, or if X is uniformly Gâteaux smooth and embeds isometrically into a Banach space with a 1-unconditional finite-dimensional decomposition.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Lens, Université d’Artois, Rue Jean Souvraz S. P. 18, 62307, Lens, France

    Pascal Lefèvre, Étienne Matheron & Armel Primot

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  1. Pascal Lefèvre
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  2. Étienne Matheron
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  3. Armel Primot
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Correspondence to Pascal Lefèvre.

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Lefèvre, P., Matheron, É. & Primot, A. Smoothness, asymptotic smoothness and the Blum-Hanson property. Isr. J. Math. 211, 271–309 (2016). https://doi.org/10.1007/s11856-015-1266-5

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  • DOI: https://doi.org/10.1007/s11856-015-1266-5

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