This is an announcement for the paper “On Garling sequence spaces” by Fernando Albiachttps://arxiv.org/find/math/1/au:+Albiac_F/0/1/0/all/0/1, José L. Ansorenahttps://arxiv.org/find/math/1/au:+Ansorena_J/0/1/0/all/0/1, Ben Wallishttps://arxiv.org/find/math/1/au:+Wallis_B/0/1/0/all/0/1.

Abstract: The aim of this paper is to introduce and investigate a new class of separable Banach spaces modeled after an example of Garling from 1968. For each $1\leq p<\infty$ and each nonincreasing weight $w\in c_0-\ell_1$ we exhibit an $\ell_p$-saturated, complementably homogeneous, and uniformly subprojective Banach space $g(w,p)$. We also show that $g(w,p)$ admits a unique subsymmetric basis despite the fact that for a wide class of weights it does not admit a symmetric basis. This provides the first known examples of Banach spaces where those two properties coexist.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1703.07772