The Gelfand–Phillips and Dunford–Pettis type properties in bimodules of measurable operators

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-02-07 DOI:10.1090/tran/9117

Jinghao Huang, Yerlan Nessipbayev, Marat Pliev, Fedor Sukochev

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引用次数: 0

Abstract

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

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可测算子双模中的格尔芬-菲利普斯和邓福德-佩蒂斯类型特性

我们完整地描述了非交换对称空间 E ( M , τ ) E(\mathcal {M},\tau ) 的特征，它隶属于一个半有限冯-诺依曼代数 M \mathcal {M} ，在一个（不一定是可分离的）具有格尔芬-菲利普斯性质和 WCG 性质的希尔伯特空间上配备了一个忠实的正态半有限迹 τ \tau 。它们与其他经典结构性质（如邓福德-佩提斯性质、舒尔性质及其变体）的关系的完整列表是在非交换对称空间的一般环境中给出的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.