Embeddings between Lorenz sequence spaces are strictly singular

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.

No reviews yet.

No comments yet.