{"title":"The joint numerical range of commuting matrices","authors":"Pan-shun Lau, Chi-Kwong Li, Y. Poon","doi":"10.4064/sm200622-31-5","DOIUrl":null,"url":null,"abstract":". It is shown that for n ≤ 3 the joint numerical range of a family of commuting n × n complex matrices is always convex; for n ≥ 4 there are two commuting matrices whose joint numerical range is not convex.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm200622-31-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
. It is shown that for n ≤ 3 the joint numerical range of a family of commuting n × n complex matrices is always convex; for n ≥ 4 there are two commuting matrices whose joint numerical range is not convex.
期刊介绍：
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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