Embeddings between Lorenz sequence spaces are strictly singular

Abstract

Given $0<p,q,r<\infty$ and $q<r\le \infty$ we consider the natural embedding ${\ell }_{p,q}\hookrightarrow {\ell }_{p,r}$ between Lorenz sequence spaces. We prove that this non-compact embedding is always strictly singular but not finitely strictly singular.

19 pages

References in corpus (1)

• On the properties of quasi-Banach function spaces