On Garling sequence spaces

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 $1⩽p<\infty$ and each nonincreasing weight $\text{w}\in c_0\setminus {\ell }_1$ we exhibit an ${\ell }_p$-saturated, complementably homogeneous, and uniformly subprojective Banach space $g(\text{w},p)$. We also show that $g(\text{w},p)$ 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.

25 pages