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

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.