This is an announcement for the paper “Isometric embedding of $\ell_1$ into Lipschitz-free spaces and $\ell_\infty$ into their duals” by Marek Cuth and Michal Johanis.

Abstract: We show that the dual of every infinite-dimensional Lipschitz-free Banach space contains an isometric copy of $\ell_{\infty}$ and that it is often the case that a Lipschitz-free Banach space contains a $1$-complemented subspace isometric to $\ell_1$. Even though we do not know whether the latter is true for every infinite-dimensional Lipschitz-free Banach space, we show that the space is never rotund. Further, in the last section we survey the relations between "isometric embedding of $\ell_{\infty}$ into the dual" and "containing as good copy of $\ell_1$ as possible" in a general Banach space.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1604.04131