This is an announcement for the paper “Nonlinear weakly sequentially continuous embeddings between Banach spaces” by Bruno de Mendonça Bragahttps://arxiv.org/find/math/1/au:+Braga_B/0/1/0/all/0/1.
Abstract: In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space $X$ coarsely (resp. uniformly) embeds into a Banach space $Y$ by a weakly sequentially continuous map, then every spreading model $(e_n)_n$ of a normalized weakly null sequence in $X$ satisfies $$|e_1+…+e_k|_{\bar{\delta_Y}\leq|e_1+…+e_k|_S$$, where $\bar{\delta_Y}$ is the modulus of asymptotic uniform convexity of $Y$. Among other results, we obtain Banach spaces $X$ and $Y$ so that $X$ coarsely (resp. uniformly) embeds into $Y$, but so that $X$ cannot be mapped into $Y$ by a weakly sequentially continuous coarse (resp. uniform) embedding.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1710.07852