%0 Journal Article
%A Pellegrino, Daniel
%A Seoane-Sepúlveda, Juan B.
%T Grothendieck's theorem for absolutely summing multilinear operators is optimal
%D 2015
%@ 0308-1087
%U https://hdl.handle.net/20.500.14352/23017
%X Grothendieck's theorem asserts that every continuous linear operator from ℓ1 to ℓ2 is absolutely (1;1)-summing. In this note we prove that the optimal constant gm so that every continuous m-linear operator from ℓ1×⋯×ℓ1 to ℓ2 is absolutely (gm;1)-summing is 2m+1. We also show that if gm<2m+1 there is c dimensional linear space composed by continuous non absolutely (gm;1)-summing m-linear operators from ℓ1×⋯×ℓ1 to ℓ2. In particular, our result solves (in the positive) a conjecture posed by A.T. Bernardino in 2011.
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