{"title":"关于线性化的技巧","authors":"G. Pisier","doi":"10.4171/LEM/64-3/4-5","DOIUrl":null,"url":null,"abstract":"In several situations, mainly involving the unitary generators of a $C^*$-algebra, we show that any matrix polynomial in the generators and the unit that is in the open unit ball can be written as a product of matrix polynomials of degree 1 also in the open unit ball.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"196 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"On a linearization trick\",\"authors\":\"G. Pisier\",\"doi\":\"10.4171/LEM/64-3/4-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In several situations, mainly involving the unitary generators of a $C^*$-algebra, we show that any matrix polynomial in the generators and the unit that is in the open unit ball can be written as a product of matrix polynomials of degree 1 also in the open unit ball.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"196 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/LEM/64-3/4-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/LEM/64-3/4-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In several situations, mainly involving the unitary generators of a $C^*$-algebra, we show that any matrix polynomial in the generators and the unit that is in the open unit ball can be written as a product of matrix polynomials of degree 1 also in the open unit ball.
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