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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the dimension of the $ l\sp{n}\sb{p}$-subspaces of Banach spaces, for $ 1\leq p<2$

Author: Gilles Pisier
Journal: Trans. Amer. Math. Soc. 276 (1983), 201-211
MSC: Primary 46B20; Secondary 60B11
MathSciNet review: 684503
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Abstract: We give an estimate relating the stable type $ p$ constant of a Banach space $ X$ with the dimension of the $ l_p^n$-subspaces of $ X$. Precisely, let $ C$ be this constant and assume $ 1 < p < 2$. We show that, for each $ \varepsilon > 0,X$ must contain a subspace $ (1 + \varepsilon )$-isomorphic to $ l_p^k$, for every $ k$ less than $ \delta (\varepsilon ){C^{p^{\prime}}}$ where $ \delta (\varepsilon ) > 0$ is a number depending only on $ p$ and $ \varepsilon $.

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Keywords: Finite-dimensional $ {l_p}$-spaces, stable type $ p$ Banach spaces, $ p$-stable vector valued random variables
Article copyright: © Copyright 1983 American Mathematical Society

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