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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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