{"title":"在希尔伯特空间上紧凑算子的理想中取值的算子值函数的弱可积分性","authors":"Matija Milović","doi":"10.1007/s11117-024-01047-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we provide some sufficient conditions for Pettis integrability of operator valued functions that take values in ideals of compact operators on the separable Hilbert space. Additionally, we show that, in general, these conditions do not imply Bochner integrability.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak integrability of operator valued functions with values in ideals of compact operators on Hilbert space\",\"authors\":\"Matija Milović\",\"doi\":\"10.1007/s11117-024-01047-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we provide some sufficient conditions for Pettis integrability of operator valued functions that take values in ideals of compact operators on the separable Hilbert space. Additionally, we show that, in general, these conditions do not imply Bochner integrability.</p>\",\"PeriodicalId\":54596,\"journal\":{\"name\":\"Positivity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-13\",\"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/s11117-024-01047-2\",\"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/s11117-024-01047-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Weak integrability of operator valued functions with values in ideals of compact operators on Hilbert space
In this paper, we provide some sufficient conditions for Pettis integrability of operator valued functions that take values in ideals of compact operators on the separable Hilbert space. Additionally, we show that, in general, these conditions do not imply Bochner integrability.
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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