{"title":"乘积伊顿三元组上von neumann型不等式的细化","authors":"M. Niezgoda","doi":"10.13001/ela.2023.7375","DOIUrl":null,"url":null,"abstract":"In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where $ V $ is a real inner product space, $ G $ is a compact subgroup of the orthogonal group $ O (V) $, and $ D \\subset V $ is a closed convex cone. By using an inner structure of an Eaton triple, a refinement of this inequality is shown. In the special case $ G = O ( V ) $, a refinement of the Cauchy-Schwarz inequality is obtained.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Refinement of von Neumann-type inequalities on product Eaton triples\",\"authors\":\"M. Niezgoda\",\"doi\":\"10.13001/ela.2023.7375\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where $ V $ is a real inner product space, $ G $ is a compact subgroup of the orthogonal group $ O (V) $, and $ D \\\\subset V $ is a closed convex cone. By using an inner structure of an Eaton triple, a refinement of this inequality is shown. In the special case $ G = O ( V ) $, a refinement of the Cauchy-Schwarz inequality is obtained.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2023.7375\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2023.7375","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了Eaton三元组$ (V,G,D) $上的一个von neumann型不等式,其中$ V $是一个实内积空间,$ G $是正交组$ O (V) $的紧子群,$ D \子集V $是一个闭凸锥。利用Eaton三元组的内部结构,给出了这个不等式的一个改进。在特殊情况$ G = O (V) $下,得到了Cauchy-Schwarz不等式的一个改进。
Refinement of von Neumann-type inequalities on product Eaton triples
In this paper, a von Neumann-type inequality is studied on an Eaton triple $ (V,G,D) $, where $ V $ is a real inner product space, $ G $ is a compact subgroup of the orthogonal group $ O (V) $, and $ D \subset V $ is a closed convex cone. By using an inner structure of an Eaton triple, a refinement of this inequality is shown. In the special case $ G = O ( V ) $, a refinement of the Cauchy-Schwarz inequality is obtained.
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