(Non-)Dunford–Pettis operators on noncommutative symmetric spaces

Jinghao Huang; Marat Pliev; Fedor Sukochev

doi:10.1016/j.jfa.2022.109443

(Non-)Dunford–Pettis operators on noncommutative symmetric spaces

Jinghao Huang^*
, Marat Pliev
, Fedor Sukochev

^*Corresponding author for this work

University of New South Wales
North Ossetian State University

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

2 Scopus citations

Abstract

We fully characterize the class of von Neumann algebras M (on a separable Hilbert space) such that any non-Dunford–Pettis operator on the predual M_⁎ fixes a copy of ⊕_ℓ₁(ℓ₂), which extends results due to Bourgain [9] and Rosenthal [49]. We also fully characterize those noncommutative symmetric spaces affiliated with different types of von Neumann algebras, which have the Dunford–Pettis property. This extends earlier results for the special cases (e.g., for symmetric function spaces, and von Neumann algebras and their preduals), by Bunce [11], by Chu and Iochum [15], and by Kaminska and Mastylo [36]. Finally, we supply new examples of symmetric spaces with the DPP on general (non-resonant) σ-finite measure spaces.

Original language	English
Article number	109443
Journal	Journal of Functional Analysis
Volume	282
Issue number	11
DOIs	https://doi.org/10.1016/j.jfa.2022.109443
State	Published - 1 Jun 2022
Externally published	Yes

Keywords

(Non-)Dunford–Pettis operator
Dunford–Pettis property
Noncommutative symmetric space
Predual of a von Neumann algebra

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10.1016/j.jfa.2022.109443

Cite this

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title = "(Non-)Dunford–Pettis operators on noncommutative symmetric spaces",

abstract = "We fully characterize the class of von Neumann algebras M (on a separable Hilbert space) such that any non-Dunford–Pettis operator on the predual M⁎ fixes a copy of ⊕ℓ1(ℓ2), which extends results due to Bourgain [9] and Rosenthal [49]. We also fully characterize those noncommutative symmetric spaces affiliated with different types of von Neumann algebras, which have the Dunford–Pettis property. This extends earlier results for the special cases (e.g., for symmetric function spaces, and von Neumann algebras and their preduals), by Bunce [11], by Chu and Iochum [15], and by Kaminska and Mastylo [36]. Finally, we supply new examples of symmetric spaces with the DPP on general (non-resonant) σ-finite measure spaces.",

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T1 - (Non-)Dunford–Pettis operators on noncommutative symmetric spaces

AU - Huang, Jinghao

AU - Pliev, Marat

AU - Sukochev, Fedor

PY - 2022/6/1

Y1 - 2022/6/1

N2 - We fully characterize the class of von Neumann algebras M (on a separable Hilbert space) such that any non-Dunford–Pettis operator on the predual M⁎ fixes a copy of ⊕ℓ1(ℓ2), which extends results due to Bourgain [9] and Rosenthal [49]. We also fully characterize those noncommutative symmetric spaces affiliated with different types of von Neumann algebras, which have the Dunford–Pettis property. This extends earlier results for the special cases (e.g., for symmetric function spaces, and von Neumann algebras and their preduals), by Bunce [11], by Chu and Iochum [15], and by Kaminska and Mastylo [36]. Finally, we supply new examples of symmetric spaces with the DPP on general (non-resonant) σ-finite measure spaces.

AB - We fully characterize the class of von Neumann algebras M (on a separable Hilbert space) such that any non-Dunford–Pettis operator on the predual M⁎ fixes a copy of ⊕ℓ1(ℓ2), which extends results due to Bourgain [9] and Rosenthal [49]. We also fully characterize those noncommutative symmetric spaces affiliated with different types of von Neumann algebras, which have the Dunford–Pettis property. This extends earlier results for the special cases (e.g., for symmetric function spaces, and von Neumann algebras and their preduals), by Bunce [11], by Chu and Iochum [15], and by Kaminska and Mastylo [36]. Finally, we supply new examples of symmetric spaces with the DPP on general (non-resonant) σ-finite measure spaces.

KW - (Non-)Dunford–Pettis operator

KW - Dunford–Pettis property

KW - Noncommutative symmetric space

KW - Predual of a von Neumann algebra

UR - https://www.scopus.com/pages/publications/85125896384

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DO - 10.1016/j.jfa.2022.109443

M3 - 文章

AN - SCOPUS:85125896384

SN - 0022-1236

VL - 282

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 11

M1 - 109443

ER -

(Non-)Dunford–Pettis operators on noncommutative symmetric spaces

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Keywords

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