Isometric embeddings of noncommutative L_p-spaces into noncommutative symmetric spaces

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 ℳ on a separable Hilbert space, if a symmetric quasi-Banach function space $E(0,1) $ containing the function t↦ t^−1/p, $0<t\le 1, $ then there exists a noncommutative probability space (𝒩,σ) such that L_p(ℳ) is isometric to a subspace of E(𝒩,σ). In particular, this answers two questions raised by Randrianantoanina in 2006.

ISOMETRIC EMBEDDING OF NONCOMMUTATIVE L_p -SPACES INTO NONCOMMUTATIVE SYMMETRIC SPACES
Jinghao Huang, Marius Junge, Fedor Sukochev +1
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BibTeX RIS

BibTeX

@misc{huang2026isometric,
  title = {{Isometric embeddings of noncommutative $L_p$-spaces into noncommutative symmetric spaces}},
  author = {Jinghao Huang and Marius Junge and Fedor Sukochev and Dmitriy Zanin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27827},
  eprint = {2609.27827},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27827},
}

RIS

TY  - UNPB
TI  - Isometric embeddings of noncommutative L_p-spaces into noncommutative symmetric spaces
AU  - Jinghao Huang
AU  - Marius Junge
AU  - Fedor Sukochev
AU  - Dmitriy Zanin
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.27827
UR  - https://arxiv.org/abs/2609.27827
AB  - 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 ℳ on a separable Hilbert space, if a symmetric quasi-Banach function space $E(0,1) $ containing the function t↦ t^−1/p, $0<t\le 1, $ then there exists a noncommutative probability space (𝒩,σ) such that L_p(ℳ) is isometric to a subspace of E(𝒩,σ). In particular, this answers two questions raised by Randrianantoanina in 2006.
ER  -

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