The Rademacher cotype of operators from 𝑙^{𝑁}_{∞}

Montgomery-Smith, S. J.; Talagrand, M.

doi:10.1090/S0002-9939-1991-1043416-X

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
DOI: https://doi.org/10.1090/S0002-9939-1991-1043416-X
MathSciNet review: 1043416
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Abstract: We show that for any operator $T:l_\infty ^N \to Y$ , where is a Banach space, its cotype 2 constant, ${K^{(2)}}(T)$ , is related to its -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

-summing.

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