{"title":"巴拿赫网格中正则 P 运算符的包络规范","authors":"Safak Alpay, Eduard Emelyanov, Svetlana Gorokhova","doi":"10.1007/s11117-024-01055-2","DOIUrl":null,"url":null,"abstract":"<p>The span of positive linear operators belonging to an operator linear class P and acting between Banach lattices is rarely a Banach space under the operator norm. We investigate the enveloping norm <span>\\(\\Vert S\\Vert _{\\text {r-P}}=\\inf \\{\\Vert T\\Vert : \\pm S\\le T\\in \\text {P}\\}\\)</span> on <span>\\({\\text {span}}(\\text {P}_+(E,F))\\)</span> that is complete under rather mild assumptions on P.\n</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Enveloping norms of regularly P-operators in Banach lattices\",\"authors\":\"Safak Alpay, Eduard Emelyanov, Svetlana Gorokhova\",\"doi\":\"10.1007/s11117-024-01055-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The span of positive linear operators belonging to an operator linear class P and acting between Banach lattices is rarely a Banach space under the operator norm. We investigate the enveloping norm <span>\\\\(\\\\Vert S\\\\Vert _{\\\\text {r-P}}=\\\\inf \\\\{\\\\Vert T\\\\Vert : \\\\pm S\\\\le T\\\\in \\\\text {P}\\\\}\\\\)</span> on <span>\\\\({\\\\text {span}}(\\\\text {P}_+(E,F))\\\\)</span> that is complete under rather mild assumptions on P.\\n</p>\",\"PeriodicalId\":54596,\"journal\":{\"name\":\"Positivity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Positivity\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11117-024-01055-2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Positivity","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11117-024-01055-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
属于算子线性类 P 并作用于巴拿赫网格之间的正线性算子的跨度很少是算子规范下的巴拿赫空间。我们研究了包络规范 \(\Vert S\Vert _{\text {r-P}}=\inf \{\Vert T\Vert ：\)上的({\text{span}}(\text {P}_+(E,F))\) 在关于 P 的相当温和的假设下是完整的。
Enveloping norms of regularly P-operators in Banach lattices
The span of positive linear operators belonging to an operator linear class P and acting between Banach lattices is rarely a Banach space under the operator norm. We investigate the enveloping norm \(\Vert S\Vert _{\text {r-P}}=\inf \{\Vert T\Vert : \pm S\le T\in \text {P}\}\) on \({\text {span}}(\text {P}_+(E,F))\) that is complete under rather mild assumptions on P.
期刊介绍：
The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome.
The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.
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