Cotype and nonlinear absolutely summing mappings

Details Cotype and nonlinear absolutely summing mappings Cotype and nonlinear absolutely summing mappings

2003-07-23

arxiv.org/abs/math/0307311v1

Mathematics

Functional Analysis

Scientific paper

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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