This is an announcement for the paper "Grothendieck's theorem for absolutely summing multilinear operators is optimal" by Daniel Pellegrino and Juan B. Seoane-Sepulveda.

Abstract: Grothendieck's theorem asserts that every continuous linear operator from $\ell_{1}$ to $\ell_{2}$ is absolutely $\left( 1;1\right) $-summing. In this note we prove that the optimal constant $g_{m}$ so that every continuous $m$-linear operator from $\ell_{1}\times\cdots\times\ell_{1}$ to $\ell_{2}$ is absolutely $\left(g_{m};1\right) $-summing is $\frac{2}{m+1}$. This result solves (in the positive) a conjecture posed by A.T. Bernardino in 2011.

Archive classification: math.FA

Submitted from: pellegrino@pq.cnpq.br

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1307.4809

or

http://arXiv.org/abs/1307.4809