{"title":"qq$ 的饱满度 -阿拉基-伍兹系数","authors":"Manish Kumar, Simeng Wang","doi":"10.1112/jlms.12989","DOIUrl":null,"url":null,"abstract":"<p>The <span></span><math>\n <semantics>\n <mi>q</mi>\n <annotation>$q$</annotation>\n </semantics></math>-Araki-Woods factor associated to a group of orthogonal transformations on a real separable Hilbert space <span></span><math>\n <semantics>\n <msub>\n <mi>H</mi>\n <mi>R</mi>\n </msub>\n <annotation>$\\mathsf {H}_{\\mathbb {R}}$</annotation>\n </semantics></math> is full as soon as <span></span><math>\n <semantics>\n <mrow>\n <mo>dim</mo>\n <msub>\n <mi>H</mi>\n <mi>R</mi>\n </msub>\n <mo>⩾</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$\\dim \\mathsf {H}_{\\mathbb {R}}\\geqslant 2$</annotation>\n </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fullness of \\n \\n q\\n $q$\\n -Araki-Woods factors\",\"authors\":\"Manish Kumar, Simeng Wang\",\"doi\":\"10.1112/jlms.12989\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The <span></span><math>\\n <semantics>\\n <mi>q</mi>\\n <annotation>$q$</annotation>\\n </semantics></math>-Araki-Woods factor associated to a group of orthogonal transformations on a real separable Hilbert space <span></span><math>\\n <semantics>\\n <msub>\\n <mi>H</mi>\\n <mi>R</mi>\\n </msub>\\n <annotation>$\\\\mathsf {H}_{\\\\mathbb {R}}$</annotation>\\n </semantics></math> is full as soon as <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>dim</mo>\\n <msub>\\n <mi>H</mi>\\n <mi>R</mi>\\n </msub>\\n <mo>⩾</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$\\\\dim \\\\mathsf {H}_{\\\\mathbb {R}}\\\\geqslant 2$</annotation>\\n </semantics></math>.</p>\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12989\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12989","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
当 dim H R ⩾ 2 $\dim \mathsf {H}_{\mathbb {R}}\geqslant 2$ 时，与实可分离希尔伯特空间 H R $\mathsf {H}_{\mathbb {R}} 上的正交变换组相关的 q $q$ -Araki-Woods 因子就是完整的。
期刊介绍：
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.
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