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Banach Spaces with Property (M) and their Szlenk Indices

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Abstract.

We show that a separable Banach space with property (M*) has a Szlenk index equal to ω0, and a norm with an optimal modulus of asymptotic uniform smoothness. From this we derive a condition on the Szlenk functions of the space and its dual which characterizes embeddability into c 0 or an ℓ p -sum of finite dimensional spaces. We also prove that two Lipschitz-isomorphic Orlicz sequence spaces contain the same ℓ p -spaces.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208016, India

    Sudipta Dutta

  2. IMJ - Projet Analyse Fonctionnelle, Université Paris 6, Boîte 186, 4 place Jussieu, 75252, Paris Cédex 05, France

    Alexandre Godard

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  1. Sudipta Dutta
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  2. Alexandre Godard
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Correspondence to Alexandre Godard.

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Dutta, S., Godard, A. Banach Spaces with Property (M) and their Szlenk Indices. MedJM 5, 211–220 (2008). https://doi.org/10.1007/s00009-008-0145-2

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  • DOI: https://doi.org/10.1007/s00009-008-0145-2

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