{"title":"2-LOCAL ISOMETRIES OF SOME NEST ALGEBRAS","authors":"BO YU, JIANKUI LI","doi":"10.1017/s000497272300117x","DOIUrl":null,"url":null,"abstract":"<p>Let <span>H</span> be a complex separable Hilbert space with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$\\dim H \\geq 2$</span></span></img></span></span>. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$\\mathcal {N}$</span></span></img></span></span> be a nest on <span>H</span> such that <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$E_+ \\neq E$</span></span></img></span></span> for any <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$E \\neq H, E \\in \\mathcal {N}$</span></span></img></span></span>. We prove that every 2-local isometry of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216090148228-0567:S000497272300117X:S000497272300117X_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$\\operatorname {Alg}\\mathcal {N}$</span></span></img></span></span> is a surjective linear isometry.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s000497272300117x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let H be a complex separable Hilbert space with $\dim H \geq 2$. Let $\mathcal {N}$ be a nest on H such that $E_+ \neq E$ for any $E \neq H, E \in \mathcal {N}$. We prove that every 2-local isometry of $\operatorname {Alg}\mathcal {N}$ is a surjective linear isometry.
期刊介绍：
Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way.
Published Bi-monthly
Published for the Australian Mathematical Society
$\dim H \geq 2$. Let 
$\mathcal {N}$ be a nest on H such that 
$E_+ \neq E$ for any 
$E \neq H, E \in \mathcal {N}$. We prove that every 2-local isometry of 
$\operatorname {Alg}\mathcal {N}$ is a surjective linear isometry.
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