Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Sergei Astashkin; Jinghao Huang; Fedor Sukochev

doi:10.1016/j.jfa.2020.108895

paper

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

arXiv:2007.03907 · doi:10.1016/j.jfa.2020.108895

Abstract

Let $E (0, 1)$ be a symmetric space on $(0, 1)$ and $C_{F}$ be a symmetric ideal of compact operators on the Hilbert space $ℓ_{2}$ associated with a symmetric sequence space $F$ . We give several criteria for $E (0, 1)$ and $F$ so that $E (0, 1)$ does not embed into the ideal $C_{F}$ , extending the result for the case when $E (0, 1) = L_{p} (0, 1)$ and $F = ℓ_{p}$ , $1 \leq p < \infty$ , due to Arazy and Lindenstrauss.