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

Stephen J. Montgomery-Smith; Michel Talagrand

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

Functional Analysis 2008-02-03 v2

Authors: Stephen J. Montgomery-Smith , Michel Talagrand

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, $\pi_{2,1}(T)$ , by $K_2(T) \le c \log\log N \pi_{2,1}(T)$ . Thus, we can show that there is an operator $T:C(K)\to Y$ that has cotype 2, but is not 2-summing.

Keywords

rademacher cotype operator banach space cotype 2 constant summing norm

Cite

@article{arxiv.math/9201207,
  title  = {The Rademacher cotype of operators from $l_\infty^N$},
  author = {Stephen J. Montgomery-Smith and Michel Talagrand},
  journal= {arXiv preprint arXiv:math/9201207},
  year   = {2008}
}

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