This is an announcement for the paper “Non-ergodic Banach spaces are near Hilbert” by W. Cuellar-Carrerahttps://arxiv.org/find/math/1/au:+Cuellar_Carrera_W/0/1/0/all/0/1.

Abstract: We prove that a non ergodic Banach space must be near Hilbert. In particular, $\ell_p$ $(2<p<\infty)$ is ergodic. This reinforces the conjecture that $\el_2$ is the only non ergodic Banach space. As an application of our criterion for ergodicity, we prove that there is no separable Banach space which is complementably universal for the class of all subspaces of $\ell_p$, for $1\leq p<2$. This solves a question left open by W. B. Johnson and A. Szankowski in 1976.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1611.05500