This is an announcement for the paper "Spaceability and optimal estimates for summing multilinear operators" by Gustavo Araujo and Daniel Pellegrino.

Abstract: We show that given a positive integer $m$, a real number $p\in\left[ 2,\infty\right) $ and $1\leq s<p^{\ast}$ the set of non--multiple $\left( r,s\right) $--summing $m$--linear forms on $\ell_{p}\times\cdots\times\ell_{p}$ is spaceable whenever $r<\frac{2ms}{s+2m-ms}$. This result is optimal since for $r\geq\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\ell _{p}\times\cdots\times\ell_{p}$ are multiple $\left( r,s\right) $--summing. Among other results, we improve some results from \cite{laa} and generalize a result related to cotype (from 2010) due to Botelho, Michels and the second named author. We also prove some new coincidence results for the class of absolutely summing multilinear operators.

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/1403.6064

or

http://arXiv.org/abs/1403.6064