Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},\tau)$ over a noncommutative probability space

Jinghao Huang; Olga Sadovskaya; Fedor Sukochev; Dmitriy Zanin

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arXiv · 2404.06761

Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},\tau)$ over a noncommutative probability space

Jinghao Huang·Olga Sadovskaya·Fedor Sukochev·Dmitriy Zanin

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Abstract

We prove that the sequence space $\ell_{p,q}$ does not embed into $L_{p,q}(\mathcal{M},\tau)$ for any noncommutative probability space $(\mathcal{M},\tau)$, $1< p<\infty $, $1\le q<\infty$, $p\ne q$. Several applications to the isomorphic classification of noncommutative $L_{p,q}$-spaces are given, which extend and complement several earlier results.

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Jinghao Huang, Olga Sadovskaya, Fedor Sukochev, Dmitriy Zanin. 2024-04-10. Lack of isomorphic embeddings of $\ell_{p,q}$ into $L_{p,q}(\mathcal{M},\tau)$ over a noncommutative probability space. https://arxiv.org/abs/2404.06761

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