THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS

Jinghao Huang; Yerlan Nessipbayev; Marat Pliev; Fedor Sukochev

doi:10.1090/tran/9117

THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS

Jinghao Huang
, Yerlan Nessipbayev
, Marat Pliev
, Fedor Sukochev

Institute for Advanced Study in Mathematics
University of New South Wales
Institute of Mathematics and Mathematical Modelling
Russian Academy of Sciences
North Ossetian State University

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

2 Scopus citations

Abstract

We fully characterize noncommutative symmetric spaces E(M, τ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace τ on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.

Original language	English
Pages (from-to)	6097-6149
Number of pages	53
Journal	Transactions of the American Mathematical Society
Volume	377
Issue number	9
DOIs	https://doi.org/10.1090/tran/9117
State	Published - Sep 2024
Externally published	Yes

Keywords

(weak/strong) Dunford–Pettis property
Gelfand–Phillips space
Noncommutative symmetric space
WCG-space
order continuous norm

Access to Document

10.1090/tran/9117

Cite this

@article{6c41ea344c4043639dbb6b45059b4be8,

title = "THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS",

abstract = "We fully characterize noncommutative symmetric spaces E(M, τ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace τ on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.",

keywords = "(weak/strong) Dunford–Pettis property, Gelfand–Phillips space, Noncommutative symmetric space, WCG-space, order continuous norm",

author = "Jinghao Huang and Yerlan Nessipbayev and Marat Pliev and Fedor Sukochev",

note = "Publisher Copyright: {\textcopyright}2024 American Mathematical Society.",

year = "2024",

month = sep,

doi = "10.1090/tran/9117",

language = "英语",

volume = "377",

pages = "6097--6149",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "9",

}

TY - JOUR

T1 - THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS

AU - Huang, Jinghao

AU - Nessipbayev, Yerlan

AU - Pliev, Marat

AU - Sukochev, Fedor

PY - 2024/9

Y1 - 2024/9

N2 - We fully characterize noncommutative symmetric spaces E(M, τ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace τ on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.

AB - We fully characterize noncommutative symmetric spaces E(M, τ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace τ on a (not necessarily separable) Hilbert space having the Gelfand–Phillips property and the WCG-property. The complete list of their relations with other classical structural properties (such as the Dunford–Pettis property, the Schur property and their variations) is given in the general setting of noncommutative symmetric spaces.

KW - (weak/strong) Dunford–Pettis property

KW - Gelfand–Phillips space

KW - Noncommutative symmetric space

KW - WCG-space

KW - order continuous norm

UR - https://www.scopus.com/pages/publications/85203056278

U2 - 10.1090/tran/9117

DO - 10.1090/tran/9117

M3 - 文章

AN - SCOPUS:85203056278

SN - 0002-9947

VL - 377

SP - 6097

EP - 6149

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 9

ER -

THE GELFAND–PHILLIPS AND DUNFORD–PETTIS TYPE PROPERTIES IN BIMODULES OF MEASURABLE OPERATORS

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this