The Rademacher cotype of operators from $l_\infty^N$

Stephen J. Montgomery-Smith; Michel Talagrand

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The Rademacher cotype of operators from $l_\infty^N$

Stephen J. Montgomery-Smith·Michel Talagrand

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Abstract

We show that for any operator $T:l_\infty^N\to Y$, where $Y$ is a Banach space, that its cotype 2 constant, $K_2(T)$, is related to its $(2,1)$-summing norm, $π_{2,1}(T)$, by $K_2(T) \le c \log\log N π_{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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BibTeX RIS

Stephen J. Montgomery-Smith, Michel Talagrand. 1999-12-04. The Rademacher cotype of operators from $l_\infty^N$. https://arxiv.org/abs/math/9201207

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