This is an announcement for the paper “Non-expansive bijections to the unit ball of $\ell_1$-sum of strictly convex Banach spaces” by Vladimir Kadetshttps://arxiv.org/find/math/1/au:+Kadets_V/0/1/0/all/0/1, Olesia Zavarzinahttps://arxiv.org/find/math/1/au:+Zavarzina_O/0/1/0/all/0/1.
Abstract: Extending recent results by Cascales, Kadets, Orihuela and Wingler (2016), Kadets and Zavarzina (2017), and Zavarzina (2017) we demonstrate that for every Banach space $X$ and every collection $Z_i, i\in I$ of strictly convex Banach spaces every non-expansive bijection from the unit ball of $X$ to the unit ball of sum of $Z_i$ by $\ell_1$ is an isometry.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1711.00262