Stephen Montgomery-Smith and Michel Talagrand, The Rademacher cotype of operators from \(\ell_\infty^N\). Proc. A.M.S. 112 (1991), 187-194. We show that for any operator \(T:\ell_\infty^N \to Y\), 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. (tex, dvi, ps, pdf.)

 

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