Embeddings between Lorentz sequence spaces are strictly but not finitely strictly singular
Volume 272 / 2023
Studia Mathematica 272 (2023), 35-57
MSC: Primary 47B06; Secondary 54C25, 46E30.
DOI: 10.4064/sm220822-10-1
Published online: 1 March 2023
Abstract
Given $0 \lt p,q, r \lt \infty $ and $ q \lt r\le \infty $ we consider the natural embedding $\ell _{p,q}\hookrightarrow \ell _{p,r}$ between Lorentz sequence spaces. We introduce a new method of proving that this non-compact embedding is always strictly singular but not finitely strictly singular.
