{"title":"投影对的广义铅笔的特征","authors":"Tao Chen, Weining Lai, Chunyuan Deng","doi":"10.1007/s43037-023-00322-w","DOIUrl":null,"url":null,"abstract":"<p>Let <i>T</i> be a bounded linear operator on a complex Hilbert space <span>\\(\\mathcal {H}\\)</span>. We present some necessary and sufficient conditions for <i>T</i> to be the generalized pencil <span>\\(P + \\alpha Q +\\beta PQ\\)</span> of a pair (<i>P</i>, <i>Q</i>) of projections at some point <span>\\((\\alpha , \\beta )\\in \\mathbb {C}^2\\)</span>. The range and kernel relations of the generalized pencil <i>T</i> are studied and comments on the additional properties of some special generalized pencil are given.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterizations of generalized pencils of pairs of projections\",\"authors\":\"Tao Chen, Weining Lai, Chunyuan Deng\",\"doi\":\"10.1007/s43037-023-00322-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>T</i> be a bounded linear operator on a complex Hilbert space <span>\\\\(\\\\mathcal {H}\\\\)</span>. We present some necessary and sufficient conditions for <i>T</i> to be the generalized pencil <span>\\\\(P + \\\\alpha Q +\\\\beta PQ\\\\)</span> of a pair (<i>P</i>, <i>Q</i>) of projections at some point <span>\\\\((\\\\alpha , \\\\beta )\\\\in \\\\mathbb {C}^2\\\\)</span>. The range and kernel relations of the generalized pencil <i>T</i> are studied and comments on the additional properties of some special generalized pencil are given.</p>\",\"PeriodicalId\":55400,\"journal\":{\"name\":\"Banach Journal of Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-02-12\",\"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/s43037-023-00322-w\",\"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/s43037-023-00322-w","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
让 T 成为复希尔伯特空间（\mathcal {H}\）上的有界线性算子。我们提出了一些必要条件和充分条件，即 T 是一对（P, Q）在某个点 \((\alpha , \beta )\in \mathbb {C}^2\)上的投影的广义铅笔 \(P+\alpha Q +\beta PQ\) 。研究了广义铅笔 T 的范围和核关系，并对一些特殊广义铅笔的附加性质给出了评论。
Characterizations of generalized pencils of pairs of projections
Let T be a bounded linear operator on a complex Hilbert space \(\mathcal {H}\). We present some necessary and sufficient conditions for T to be the generalized pencil \(P + \alpha Q +\beta PQ\) of a pair (P, Q) of projections at some point \((\alpha , \beta )\in \mathbb {C}^2\). The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some special generalized pencil are given.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
