Embedding between Lebesgue and weak Lebesgue sequence spaces is strictly singular

Abstract

Given $1<p<q<\infty$ it is well know that the natural embedding of Lebesgue sequence spaces ${\ell }_p\hookrightarrow {\ell }_q$ is strictly singular. In this paper we extend this classical results and show that even the natural non-compact embedding between Lebesgue and weak Lebesgue sequence spaces ${\ell }_p\hookrightarrow {\ell }_{p,\infty }$ is strictly singular.

10 pages