Pellegrino, DanielSeoane-Sepúlveda, Juan B.2023-06-182023-06-182015-030308-108710.1080/03081087.2013.877013https://hdl.handle.net/20.500.14352/23017Grothendieck'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.engjournal articlehttp://www.tandfonline.com/doi/abs/10.1080/03081087.2013.877013#.VTDkqvmsWClhttp://arxiv.org/pdf/1307.4809v2.pdfopen access51lineabilityspaceabilityabsolutely summing operatorsMatemáticas (Matemáticas)12 Matemáticas