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

{"title":"增生耗散块矩阵的范数不等式","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":"{\"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。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Norm inequalities for accretive-dissipative block matrices

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.

期刊最新文献

New results on the existence of periodic solutions for a higher-order p -Laplacian neutral differential equation with multiple deviating arguments Markov dynamics on the cone of discrete Radon measures On one problem of Yu. M. Berezansky Equality between different types of invertibility Tensor product and variants of Weyl's type theorem for p - w -hyponormal operators