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arXiv · 2609.27827

Isometric embeddings of noncommutative $L_p$-spaces into noncommutative symmetric spaces

Jinghao Huang·Marius Junge·Fedor Sukochev·Dmitriy Zanin
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Abstract

We establish a noncommutative version of a familiar Johnson--Maurey--Schechtman--Tzafriri Theorem, by showing that for any $0 <p<2$ and a (not necessarily semifinite) von Neumann algebra $\mathcal{M}$ on a separable Hilbert space, if a symmetric quasi-Banach function space $E(0,1) $ containing the function $t\mapsto t^{-1/p}$, $0<t\le 1, $ then there exists a noncommutative probability space $(\mathcal{N},σ)$ such that $L_p(\mathcal{M})$ is isometric to a subspace of $E(\mathcal{N},σ)$. In particular, this answers two questions raised by Randrianantoanina in 2006.

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Jinghao Huang, Marius Junge, Fedor Sukochev, Dmitriy Zanin. 2026-08-27. Isometric embeddings of noncommutative $L_p$-spaces into noncommutative symmetric spaces. https://arxiv.org/abs/2609.27827

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