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On coarse embeddings into c0(Γ) (2018)

Hájek P, Schlumprecht T.

Oxford University Press

In: Quarterly Journal of Mathematics

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Publication Date: 2018-03-06

Description: Let λ be a large enough cardinal number (assuming the Generalized Continuum Hypothesis it suffices to let λ=ℵω). If X is a Banach space with dens(X)≥λ, which admits a coarse (or uniform) embedding into any c0(Γ), then X fails to have non-trivial cotype, i.e. X contains ℓ∞n C -uniformly for every C〉1. In the special case when X has a symmetric basis, we may even conclude that it is linearly isomorphic with c0(densX).

Print ISSN: 0033-5606

Electronic ISSN: 1464-3847

Topics: Mathematics

Published by Oxford University Press

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