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arXiv · 2202.04523

Unified Grothendieck's and Kwapie\'{n}'s theorems for multilinear operators

Daniel Núñez-Alarcón·Joedson Santos·Diana Serrano-Rodríguez
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Abstract

Kwapie\'{n}'s theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{p}$ is absolutely $\left( r,1\right) $-summing for $1/r=1-\left\vert 1/p-1/2\right\vert .$ When $p=2$ it recovers the famous Grothendieck's theorem. In this paper investigate multilinear variants of these theorems and related issues. Among other results we present a unified version of Kwapie\'{n}'s and Grothendieck's results that encompasses the cases of multiple summing and absolutely summing multilinear operators.

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Daniel Núñez-Alarcón, Joedson Santos, Diana Serrano-Rodríguez. 2022-02-09. Unified Grothendieck's and Kwapie\'{n}'s theorems for multilinear operators. https://arxiv.org/abs/2202.04523

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