Fadi Alrimawi, M. Al-khlyleh, F. A. Abushaheen
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{"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}
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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
增生耗散块矩阵的范数不等式
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。
来源期刊
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.
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