This is an announcement for the paper “Asymptotic properties of Banach spaces and coarse quotient maps” by Sheng Zhanghttps://arxiv.org/find/math/1/au:+Zhang_S/0/1/0/all/0/1.

Abstract: We give a quantitative result about asymptotic moduli of Banach spaces under coarse quotient maps. More precisely, we prove that if a Banach space $Y$ is a coarse quotient of a subset of a Banach space $X$, where the coarse quotient map is coarse Lipschitz, then the $(\beta)$-modulus of $X$ is bounded by the modulus of asymptotic uniform smoothness of $Y$ up to some constants.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1705.10207