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Embedding subspaces of $ L\sb 1$ into $ l\sp N\sb 1$


Author: Michel Talagrand
Journal: Proc. Amer. Math. Soc. 108 (1990), 363-369
MSC: Primary 46B25; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1990-0994792-4
MathSciNet review: 994792
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Abstract: We simplify techniques of Schechtman, Bourgain, Lindenstrauss, Milman, to prove the following. If $ X$ is an $ n$-dimensional subspace of $ {L_1}$, there exists a subspace $ Y$ of $ l_1^N$ such that $ d\left( {X,Y} \right) \leq 1 + \varepsilon $ whenever $ N \geq CK{\left( X \right)^2}{\varepsilon ^{ - 2}}n$, where $ K\left( X \right)$ is the $ K$-convexity constant of $ X$, and where $ C$ is a universal constant.


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DOI: https://doi.org/10.1090/S0002-9939-1990-0994792-4
Article copyright: © Copyright 1990 American Mathematical Society

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