{"title":"复多项式矩阵的Von Neumann不等式","authors":"Joachim Moussounda Mouanda","doi":"10.4236/ajcm.2021.114019","DOIUrl":null,"url":null,"abstract":"We prove that every matrix ( ) k n F M ∈ is associated with the smallest positive integer ( ) 1 d F ≠ such that ( ) d F F ∞ is always bigger than the sum of the operator norms of the Fourier coefficients of F. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality holds up to the constant 2 n for matrices of the algebra ( ) k n M .","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Von Neumann’s Inequality for Matrices of Complex Polynomials\",\"authors\":\"Joachim Moussounda Mouanda\",\"doi\":\"10.4236/ajcm.2021.114019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that every matrix ( ) k n F M ∈ is associated with the smallest positive integer ( ) 1 d F ≠ such that ( ) d F F ∞ is always bigger than the sum of the operator norms of the Fourier coefficients of F. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality holds up to the constant 2 n for matrices of the algebra ( ) k n M .\",\"PeriodicalId\":64456,\"journal\":{\"name\":\"美国计算数学期刊(英文)\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"美国计算数学期刊(英文)\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.4236/ajcm.2021.114019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"美国计算数学期刊(英文)","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4236/ajcm.2021.114019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明了每一个矩阵()k n F M∈都与最小的正整数()1d F≠相关联，使得()d F F∞总是大于F的傅里叶系数的算子范数之和。在应用中，我们证明了von Neumann不等式对于代数()k n M的矩阵保持常数2n。
On Von Neumann’s Inequality for Matrices of Complex Polynomials
We prove that every matrix ( ) k n F M ∈ is associated with the smallest positive integer ( ) 1 d F ≠ such that ( ) d F F ∞ is always bigger than the sum of the operator norms of the Fourier coefficients of F. We establish some inequalities for matrices of complex polynomials. In application, we show that von Neumann’s inequality holds up to the constant 2 n for matrices of the algebra ( ) k n M .
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