增生耗散块矩阵的范数不等式

IF 0.2 Q4 MATHEMATICS

Methods of Functional Analysis and Topology Pub Date : 2020-09-28 DOI:10.31392/mfat-npu26_3.2020.02

Fadi Alrimawi, M. Al-khlyleh, F. A. Abushaheen

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Also, if f is concave and increasing on [0,\\infty ) where f(0) = 0, then \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\left( \\sum i<j | Tij | \\right) + f \\left( \\sum i<j \\bigm| \\bigm| T \\ast ji\\bigm| \\bigm| 2 \\right) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\leq (2m2 2m) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\Biggl( | T | 4 \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| . ¥å © T = Tij \\in \\BbbM mn(\\BbbC ), ¤¥ Tij \\in \\BbbM n(\\BbbC ) ̄à ̈ i, j = 1, 2, ...,m., { aà¥â ̈¢®¤ ̈á ̈ ̄ â ̈¢ ¬ âà ̈æï. ¥å © f ® ̄ãa« äãaæ÷ï, ïa §à®áâ õ [0,\\infty ), ¤¥ f(0) = 0. ®¤÷ \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\left( \\sum i<j | Tij | \\right) + f \\left( \\sum i<j \\bigm| \\bigm| T \\ast ji\\bigm| \\bigm| 2 \\right) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\leq \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\biggl( m2 m 2 | T | \\biggr) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| . a®¦, ïaé® f õ ã£ãâ®î, §à®áâ õ [0,\\infty ) ÷ f(0) = 0, â® \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\left( \\sum i<j | Tij | \\right) + f \\left( \\sum i<j \\bigm| \\bigm| T \\ast ji\\bigm| \\bigm| 2 \\right) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\leq (2m2 2m) \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| f \\Biggl( | T | 4 \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| \\bigm| .","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"9 5","pages":"201-215"},"PeriodicalIF":0.2000,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Norm inequalities for accretive-dissipative block matrices\",\"authors\":\"Fadi Alrimawi, M. Al-khlyleh, F. A. Abushaheen\",\"doi\":\"10.31392/mfat-npu26_3.2020.02\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let T = [Tij ] \\\\in \\\\BbbM mn(\\\\BbbC ) be accretive-dissipative, where Tij \\\\in \\\\BbbM n(\\\\BbbC ) for i, j = 1, 2, ...,m. Let f be a function that is convex and increasing on [0,\\\\infty ) where f(0) = 0. Then \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\left( \\\\sum i<j | Tij | \\\\right) + f \\\\left( \\\\sum i<j \\\\bigm| \\\\bigm| T \\\\ast ji\\\\bigm| \\\\bigm| 2 \\\\right) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\leq \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\biggl( m2 m 2 | T | \\\\biggr) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| . Also, if f is concave and increasing on [0,\\\\infty ) where f(0) = 0, then \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\left( \\\\sum i<j | Tij | \\\\right) + f \\\\left( \\\\sum i<j \\\\bigm| \\\\bigm| T \\\\ast ji\\\\bigm| \\\\bigm| 2 \\\\right) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\leq (2m2 2m) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\Biggl( | T | 4 \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| . ¥å © T = Tij \\\\in \\\\BbbM mn(\\\\BbbC ), ¤¥ Tij \\\\in \\\\BbbM n(\\\\BbbC ) ̄à ̈ i, j = 1, 2, ...,m., { aà¥â ̈¢®¤ ̈á ̈ ̄ â ̈¢ ¬ âà ̈æï. ¥å © f ® ̄ãa« äãaæ÷ï, ïa §à®áâ õ [0,\\\\infty ), ¤¥ f(0) = 0. ®¤÷ \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\left( \\\\sum i<j | Tij | \\\\right) + f \\\\left( \\\\sum i<j \\\\bigm| \\\\bigm| T \\\\ast ji\\\\bigm| \\\\bigm| 2 \\\\right) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\leq \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\biggl( m2 m 2 | T | \\\\biggr) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| . a®¦, ïaé® f õ ã£ãâ®î, §à®áâ õ [0,\\\\infty ) ÷ f(0) = 0, â® \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\left( \\\\sum i<j | Tij | \\\\right) + f \\\\left( \\\\sum i<j \\\\bigm| \\\\bigm| T \\\\ast ji\\\\bigm| \\\\bigm| 2 \\\\right) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\leq (2m2 2m) \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| f \\\\Biggl( | T | 4 \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| \\\\bigm| .\",\"PeriodicalId\":44325,\"journal\":{\"name\":\"Methods of Functional Analysis and Topology\",\"volume\":\"9 5\",\"pages\":\"201-215\"},\"PeriodicalIF\":0.2000,\"publicationDate\":\"2020-09-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Methods of Functional Analysis and Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31392/mfat-npu26_3.2020.02\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods of Functional Analysis and Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31392/mfat-npu26_3.2020.02","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设T=[Tij]\in\BbbMmn（\BbbC）是增生耗散的，其中对于i，j=1，2。。。，m。设f是在[0，\infty）上凸且递增的函数，其中f（0）=0。然后\bigm|\bigm|| \bigm| \bigm |\bigm || \bigm | \bigm|1\bigm|3\bigm（\sum i本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Norm inequalities for accretive-dissipative block matrices

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来源期刊

Methods of Functional Analysis and Topology MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.