Diagonal extendible multilinear operators between $\ell_p$-spaces
  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 $\ell_p$. 
Daniel Carando, Ver\'onica Dimant, Pablo Sevilla-Peris and Rom\'an   Villafa\~ne
math.FA