Diagonal extendible multilinear operators between ${\ell }_p$-spaces

Abstract

We study extendibility of diagonal multilinear operators from ${\ell }_p$ to ${\ell }_q$ spaces. We determine the values of $p$ and $q$ for which every diagonal $n$-linear operator is extendible, and those for which the only extendible ones are integral. We address the same question for multilinear forms on ${\ell }_p$.