This is an announcement for the paper "Uniform openness of multiplication in Banach spaces $L _p$" by Marek Balcerzak, Adam Majchrzycki, and Filip Strobin. Abstract: We show that multiplication from $L_p\times L_q$ to $L_1$ (for $p,q\in [1,\infty]$, $1/p+1/q=1$) is a uniformly open mapping. We also prove the uniform openness of the multiplication from $\ell_1\times c_0$ to $\ell_1$. This strengthens the former results obtained by M. Balcerzak, A.~Majchrzycki and A. Wachowicz. Archive classification: math.FA Mathematics Subject Classification: 46B25, 47A06, 54C10 Remarks: 8 pages Submitted from: filip.strobin@p.lodz.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1309.3433 or http://arXiv.org/abs/1309.3433