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arXiv · 2203.07299

Embedding between Lebesgue and weak Lebesgue sequence spaces is strictly singular

Jan Lang·Aleš Nekvinda
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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.

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Jan Lang, Aleš Nekvinda. 2022-03-14. Embedding between Lebesgue and weak Lebesgue sequence spaces is strictly singular. https://arxiv.org/abs/2203.07299

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