{"title":"作用于巴拿赫空间不同 $$L^p$$ 直接积分之间的可分解算子","authors":"N. Evseev, A. Menovschikov","doi":"10.1007/s10476-024-00044-7","DOIUrl":null,"url":null,"abstract":"<div><p>The notion of decomposable operators acting between distinct <span>\\(L^p\\)</span>-direct \nintegrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a \nmapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Decomposable operators acting between distinct \\\\(L^p\\\\)-direct integrals of Banach spaces\",\"authors\":\"N. Evseev, A. Menovschikov\",\"doi\":\"10.1007/s10476-024-00044-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The notion of decomposable operators acting between distinct <span>\\\\(L^p\\\\)</span>-direct \\nintegrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a \\nmapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-024-00044-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-024-00044-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Decomposable operators acting between distinct \(L^p\)-direct integrals of Banach spaces
The notion of decomposable operators acting between distinct \(L^p\)-direct
integrals of Banach spaces is introduced. We show that these operators generalize the composition operator in the sense that a binary relation replaces a
mapping. The necessary and sufficient conditions for the boundedness of those operators are the main results of the paper.
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