This is an announcement for the paper “On coincidence results for summing multilinear operators: interpolation, $\ell_1$-spaces and cotype” by F. Bayarthttps://arxiv.org/search?searchtype=author&query=Bayart%2C+F, D. Pellegrinohttps://arxiv.org/search?searchtype=author&query=Pellegrino%2C+D, P. Ruedahttps://arxiv.org/search?searchtype=author&query=Rueda%2C+P.
Abstract: 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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1805.12500