= Cotype 2 extrapolation on finite-dimensional linfinity
If a <Banach space> $Y$ has <cotype 2> constant $C$, every <bounded linear operator> $T:\ell_\infty^N\to Y$ satisfies $\pi_2(T)\le3^{1/4}C\pi_4(T)$ and $\pi_2(T)\le4\sqrt3 C^2\|T\|$, uniformly in $N$. The first bound follows from <Pietsch factorization theorem> and the fourth moment bound for <Rademacher sums>. For the second, 2-summing domination gives a weighted coordinate $L^2$ norm; clipping coordinates at a variable threshold yields $\pi_4(T)\le2\sqrt{\|T\|\pi_2(T)}$, which absorbs the first bound.
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