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

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

1989-11-17

arxiv.org/abs/math/9201207v2

Proc. A.M.S. 112 (1991), 187-194

Mathematics

Functional Analysis

Scientific paper

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.

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