{"title":"On Haagerup noncommutative quasi Hp(A) spaces","authors":"","doi":"10.1016/j.jmaa.2024.128905","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>M</mi></math></span> be a <em>σ</em>-finite von Neumann algebra, equipped with a normal faithful state <em>φ</em>, and let <span><math><mi>A</mi></math></span> be a maximal subdiagonal subalgebra of <span><math><mi>M</mi></math></span>. We have proved that for <span><math><mn>0</mn><mo><</mo><mi>p</mi><mo><</mo><mn>1</mn></math></span>, <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> is independent of <em>φ</em>. Furthermore, in the case that <span><math><mi>A</mi></math></span> is a type 1 subdiagonal subalgebra, we have obtained an interpolation theorem for <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span> in the case where <span><math><mn>0</mn><mo><</mo><mi>θ</mi><mo><</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≤</mo><mo>∞</mo></math></span> and <span><math><mi>p</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>−</mo><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>θ</mi></mrow><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008278","RegionNum":3,"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
Abstract
Let be a σ-finite von Neumann algebra, equipped with a normal faithful state φ, and let be a maximal subdiagonal subalgebra of . We have proved that for , is independent of φ. Furthermore, in the case that is a type 1 subdiagonal subalgebra, we have obtained an interpolation theorem for in the case where , and .
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