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Cotype and nonlinear absolutely summing mappings

Daniel M. Pellegrino
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Abstract

In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every $n$% -linear mapping from $\mathcal{L}_{\infty}$-spaces into $\mathbb{K}$ is $% (2;2,...,2,\infty)$-summing and also shown that every $n$-linear mapping from $\mathcal{L}_{\infty}$-spaces into $F$ is $(q;2,...,2)$-summing whenever $F$ has cotype $q.$ We also give new examples of analytic summing mappings and polynomial and multilinear versions of a linear Extrapolation Theorem.

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Daniel M. Pellegrino. 2003-07-23. Cotype and nonlinear absolutely summing mappings. https://arxiv.org/abs/math/0307311

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