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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the dimension of the $l^{n}_{p}$-subspaces of Banach spaces, for $1\leq p<2$
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by Gilles Pisier PDF
Trans. Amer. Math. Soc. 276 (1983), 201-211 Request permission

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 $\delta (\varepsilon ){C^{p’}}$ where $\delta (\varepsilon ) > 0$ is a number depending only on $p$ and $\varepsilon$.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 276 (1983), 201-211
  • MSC: Primary 46B20; Secondary 60B11
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0684503-5
  • MathSciNet review: 684503