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Fine embeddings of finite-dimensional subspaces of $ L\sb p,\;1\leq p<2$, into $ l\sp m\sb 1$


Author: Gideon Schechtman
Journal: Proc. Amer. Math. Soc. 94 (1985), 617-623
MSC: Primary 46E30; Secondary 46B99
DOI: https://doi.org/10.1090/S0002-9939-1985-0792272-0
MathSciNet review: 792272
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Abstract: Every $ m$-dimensional subspace of $ {L_p}$, $ 1 < p < 2$, $ (1 + \varepsilon )$-embeds into $ l_1^n$ as long as $ n \geqslant \eta {m^{1 + (1/p)}}{(\log m)^{ - 1}}$, where $ \eta = \eta (p,\varepsilon ) < \infty $. For subspaces of $ {L_1}$ we get a somewhat weaker result.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792272-0
Article copyright: © Copyright 1985 American Mathematical Society

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