{"title":"The Gelfand–Phillips and Dunford–Pettis type properties in bimodules of measurable operators","authors":"Jinghao Huang, Yerlan Nessipbayev, Marat Pliev, Fedor Sukochev","doi":"10.1090/tran/9117","DOIUrl":null,"url":null,"abstract":"<p>We fully characterize noncommutative symmetric spaces <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E left-parenthesis script upper M comma tau right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">E(\\mathcal {M},\\tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> affiliated with a semifinite von Neumann algebra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">\\mathcal {M}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> equipped with a faithful normal semifinite trace <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"tau\"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding=\"application/x-tex\">\\tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/tran/9117","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.
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