  Grothendieck's theorem asserts that every continuous linear operator from
$\ell_1$ to $\ell_2$ is absolutely $(1,1)$-summing. This kind of result is
commonly called coincidence result. In this paper we investigate coincidence
results in the multilinear setting, showing how the cotype of the spaces
involved affect such results. The special role played by $\ell_1$ spaces is
also investigated with relation to interpolation of tensor products. In
particular, an open problem on the interpolation of $m$ injective tensor
products is solved.
