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

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
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.

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。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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