Lack of isomorphic embeddings of sequence space ℓp,q into Lp,q(M,τ) over a noncommutative probability space

Jinghao Huang; Olga Sadovskaya; Fedor Sukochev; Dmitriy Zanin

doi:10.1016/j.aim.2025.110571

Lack of isomorphic embeddings of sequence space ℓ_p,q into Lp,q(M,τ) over a noncommutative probability space

Jinghao Huang^*
, Olga Sadovskaya
, Fedor Sukochev
, Dmitriy Zanin

^*Corresponding author for this work

School of Mathematics

Institute of Mathematics
University of New South Wales

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the sequence space ℓp,q does not embed into Lp,q(M,τ) for any noncommutative probability space (M,τ) when 1<p<∞, 1≤q<∞ and p≠q. Several applications to the isomorphic classification of noncommutative Lp,q-spaces are given, which generalize earlier results in [31,32,36,43,61].

Original language	English
Article number	110571
Journal	Advances in Mathematics
Volume	482
DOIs	https://doi.org/10.1016/j.aim.2025.110571
State	Published - Dec 2025

Keywords

Isomorphic embedding
Noncommutative L-space
ℓ sequence space

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title = "Lack of isomorphic embeddings of sequence space ℓp,q into Lp,q(M,τ) over a noncommutative probability space",

abstract = "We prove that the sequence space ℓp,q does not embed into Lp,q(M,τ) for any noncommutative probability space (M,τ) when 1",

keywords = "Isomorphic embedding, Noncommutative L-space, ℓ sequence space",

author = "Jinghao Huang and Olga Sadovskaya and Fedor Sukochev and Dmitriy Zanin",

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doi = "10.1016/j.aim.2025.110571",

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AU - Huang, Jinghao

AU - Sadovskaya, Olga

AU - Sukochev, Fedor

AU - Zanin, Dmitriy

PY - 2025/12

Y1 - 2025/12

N2 - We prove that the sequence space ℓp,q does not embed into Lp,q(M,τ) for any noncommutative probability space (M,τ) when 1

AB - We prove that the sequence space ℓp,q does not embed into Lp,q(M,τ) for any noncommutative probability space (M,τ) when 1

KW - Isomorphic embedding

KW - Noncommutative L-space

KW - ℓ sequence space

UR - https://www.scopus.com/pages/publications/105019967429

U2 - 10.1016/j.aim.2025.110571

DO - 10.1016/j.aim.2025.110571

M3 - 文章

AN - SCOPUS:105019967429

SN - 0001-8708

VL - 482

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 110571

ER -

Lack of isomorphic embeddings of sequence space ℓ_p,q into Lp,q(M,τ) over a noncommutative probability space

Abstract

Keywords

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