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Lack of isomorphic embedding from Lorentz function spaces into Lorentz operator ideals
Abstract
In the present paper, we study the existence of isomorphic embeddings from Lorentz function spaces Lp1,q1 into Lorentz ideals 𝒞p2,q2 in B(H). In particular, we show that, for p,q∈ (0,∞), the quasi-Banach function space Lp,q(0,1) isomorphically embeds into the ideal 𝒞p,q if and only if (p,q)=(2,2). This extends several existing results in the literature and answers a question due to Astashkin et. al.
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BibTeX
@misc{huang2026lack,
title = {{Lack of isomorphic embedding from Lorentz function spaces into Lorentz operator ideals}},
author = {Jinghao Huang and Fedor Sukochev and Dmitriy Zanin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27826},
eprint = {2609.27826},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27826},
}
RIS
TY - UNPB
TI - Lack of isomorphic embedding from Lorentz function spaces into Lorentz operator ideals
AU - Jinghao Huang
AU - Fedor Sukochev
AU - Dmitriy Zanin
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.27826
UR - https://arxiv.org/abs/2609.27826
AB - In the present paper, we study the existence of isomorphic embeddings from Lorentz function spaces L_p_1,q_1 into Lorentz ideals 𝒞_p_2,q_2 in B(H). In particular, we show that, for p,q∈ (0,∞), the quasi-Banach function space L_p,q(0,1) isomorphically embeds into the ideal 𝒞_p,q if and only if (p,q)=(2,2). This extends several existing results in the literature and answers a question due to Astashkin et. al.
ER -