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

On coincidence results for summing multilinear operators: interpolation, $\ell_1$-spaces and cotype