{"title":"哈代空间上托普利兹算子或汉克尔算子的偏斜换向器","authors":"Yongning Li, Hanyi Zheng, Xuanhao Ding","doi":"10.1007/s43037-024-00330-4","DOIUrl":null,"url":null,"abstract":"<p>Let <i>A</i> and <i>B</i> be two bounded linear operators on a Hilbert space. <i>B</i> is called the skew commutator of <i>A</i> if <span>\\(_{*}[A, B]=AB-BA^{*}=0.\\)</span> In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient condition for the product of a Hankel operator and a Toeplitz operator to be self-adjoint on the Hardy space.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces\",\"authors\":\"Yongning Li, Hanyi Zheng, Xuanhao Ding\",\"doi\":\"10.1007/s43037-024-00330-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>A</i> and <i>B</i> be two bounded linear operators on a Hilbert space. <i>B</i> is called the skew commutator of <i>A</i> if <span>\\\\(_{*}[A, B]=AB-BA^{*}=0.\\\\)</span> In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient condition for the product of a Hankel operator and a Toeplitz operator to be self-adjoint on the Hardy space.</p>\",\"PeriodicalId\":55400,\"journal\":{\"name\":\"Banach Journal of Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Banach Journal of Mathematical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s43037-024-00330-4\",\"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":"Banach Journal of Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s43037-024-00330-4","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
设 A 和 B 是希尔伯特空间上的两个有界线性算子。如果 \(_{*}[A,B]=AB-BA^{*}=0.\)，则 B 称为 A 的偏斜换元子。 在本文中，我们完全描述了哈代空间上的托普利兹算子何时是汉克尔算子的偏斜换元子，以及哈代空间上的汉克尔算子何时是托普利兹算子的偏斜换元子。此外，我们还得到了汉克尔算子和托普利兹算子的乘积在哈代空间上自相交的必要条件和充分条件。
The skew commutators of Toeplitz operators or Hankel operators on Hardy spaces
Let A and B be two bounded linear operators on a Hilbert space. B is called the skew commutator of A if \(_{*}[A, B]=AB-BA^{*}=0.\) In this paper, we completely characterize when a Toeplitz operator on the Hardy space is a skew commutator of a Hankel operator and when a Hankel operator on the Hardy space is a skew commutator of a Toeplitz operator. Moreover, we also obtain a necessary and sufficient condition for the product of a Hankel operator and a Toeplitz operator to be self-adjoint on the Hardy space.
期刊介绍：
The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.
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