Lack of isomorphic embeddings of symmetric function spaces into operator ideals

S. Astashkin; J. Huang; F. Sukochev

doi:10.1016/j.jfa.2020.108895

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

S. Astashkin
, J. Huang^*
, F. Sukochev

^*Corresponding author for this work

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

5 Scopus citations

Abstract

Let E(0,1) be a symmetric space on (0,1) and C_F be a symmetric ideal of compact operators on the Hilbert space ℓ₂ associated with a symmetric sequence space F. We give several criteria for E(0,1) and F so that E(0,1) does not embed into the ideal C_F, extending the result for the case when E(0,1)=L_p(0,1) and F=ℓ_p, 1≤p<∞, due to Arazy and Lindenstrauss [5].

Original language	English
Article number	108895
Journal	Journal of Functional Analysis
Volume	280
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2020.108895
State	Published - 1 Mar 2021
Externally published	Yes

Keywords

Ideal of compact operators
Isomorphic embedding
Orlicz space
Symmetric space

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10.1016/j.jfa.2020.108895

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abstract = "Let E(0,1) be a symmetric space on (0,1) and CF be a symmetric ideal of compact operators on the Hilbert space ℓ2 associated with a symmetric sequence space F. We give several criteria for E(0,1) and F so that E(0,1) does not embed into the ideal CF, extending the result for the case when E(0,1)=Lp(0,1) and F=ℓp, 1≤p<∞, due to Arazy and Lindenstrauss [5].",

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AU - Astashkin, S.

AU - Huang, J.

AU - Sukochev, F.

PY - 2021/3/1

Y1 - 2021/3/1

N2 - Let E(0,1) be a symmetric space on (0,1) and CF be a symmetric ideal of compact operators on the Hilbert space ℓ2 associated with a symmetric sequence space F. We give several criteria for E(0,1) and F so that E(0,1) does not embed into the ideal CF, extending the result for the case when E(0,1)=Lp(0,1) and F=ℓp, 1≤p<∞, due to Arazy and Lindenstrauss [5].

AB - Let E(0,1) be a symmetric space on (0,1) and CF be a symmetric ideal of compact operators on the Hilbert space ℓ2 associated with a symmetric sequence space F. We give several criteria for E(0,1) and F so that E(0,1) does not embed into the ideal CF, extending the result for the case when E(0,1)=Lp(0,1) and F=ℓp, 1≤p<∞, due to Arazy and Lindenstrauss [5].

KW - Ideal of compact operators

KW - Isomorphic embedding

KW - Orlicz space

KW - Symmetric space

UR - https://www.scopus.com/pages/publications/85097794738

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DO - 10.1016/j.jfa.2020.108895

M3 - 文章

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SN - 0022-1236

VL - 280

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

M1 - 108895

ER -

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Abstract

Keywords

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