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

被引：1

作者：

Huang, Jinghao ^{[1
]}

Nessipbayev, Yerlan ^{[2
,3
]}

Pliev, Marat ^{[4
,5
,6
]}

Sukochev, Fedor ^{[2
,6
]}

机构：

[1] HIT, Inst Adv Study Math, Harbin 150001, Peoples R China

[2] Univ New South Wales, Sch Math & Stat, Kensington 2052, Australia

[3] Inst Math & Math Modeling, Alma Ata 050010, Kazakhstan

[4] Russian Acad Sci, Southern Math Inst, Rus 362027, Romania

[5] Russian Acad Sci, North Caucasus Ctr Math Res, Vladikavkaz Sci Ctr, Vladikavkaz 362027, Russia

[6] North Ossetian State Univ, Vladikavkaz 362025, Russia

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 377卷 / 09期

基金：

澳大利亚研究理事会;

关键词：

Noncommutative symmetric space; order continuous norm; Gelfand- Phillips space; WCG-space; (weak/strong) Dunford-Pettis property; SYMMETRIC-SPACES; WEAK COMPACTNESS; BANACH-SPACES; ASTERISK; DOMINATION; SCHUR; SETS;

D O I：

10.1090/tran/9117

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We fully characterize noncommutative symmetric spaces E ( M , tau ) affiliated with a semifinite von Neumann algebra M equipped with a faithful normal semifinite trace tau 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.

引用

页码：6097 / 6149

页数：53

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