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The Rademacher cotype of operators from $ l\sp N\sb \infty$

Authors: S. J. Montgomery-Smith and M. Talagrand
Journal: Proc. Amer. Math. Soc. 112 (1991), 187-194
MSC: Primary 46B20; Secondary 47B10, 47B37, 60G99
MathSciNet review: 1043416
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Abstract: We show that for any operator $ T:l_\infty ^N \to Y$, where $ Y$ is a Banach space, its cotype 2 constant, $ {K^{(2)}}(T)$, is related to its $ (2,1)$-summing norm, $ {\pi _{2,1}}(T)$, by

$\displaystyle {K^{(2)}}(T) \leq c\operatorname{log} \operatorname{log} N{\pi _{2,1}}(T).$

Thus, we can show that there is an operator $ T:C(K) \to Y$ that has cotype 2, but is not $ 2$-summing.

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