{"title":"不可分重排不变空间中的正交性","authors":"S. V. Astashkin, E. Semenov","doi":"10.1070/SM9543","DOIUrl":null,"url":null,"abstract":"Let be a nonseparable rearrangement-invariant space and let be the closure of the space of bounded functions in . Elements of orthogonal to , that is, elements , , such that for each , are investigated. The set of orthogonal elements is characterized in the case when is a Marcinkiewicz or an Orlicz space. If an Orlicz space is considered with the Luxemburg norm, then the set is the algebraic sum of and . Each nonseparable rearrangement-invariant space such that is shown to contain an asymptotically isometric copy of the space . Bibliography: 17 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"79 1","pages":"1553 - 1570"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orthogonality in nonseparable rearrangement-invariant spaces\",\"authors\":\"S. V. Astashkin, E. Semenov\",\"doi\":\"10.1070/SM9543\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let be a nonseparable rearrangement-invariant space and let be the closure of the space of bounded functions in . Elements of orthogonal to , that is, elements , , such that for each , are investigated. The set of orthogonal elements is characterized in the case when is a Marcinkiewicz or an Orlicz space. If an Orlicz space is considered with the Luxemburg norm, then the set is the algebraic sum of and . Each nonseparable rearrangement-invariant space such that is shown to contain an asymptotically isometric copy of the space . Bibliography: 17 titles.\",\"PeriodicalId\":49573,\"journal\":{\"name\":\"Sbornik Mathematics\",\"volume\":\"79 1\",\"pages\":\"1553 - 1570\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sbornik Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/SM9543\",\"RegionNum\":4,\"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":"Sbornik Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/SM9543","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Orthogonality in nonseparable rearrangement-invariant spaces
Let be a nonseparable rearrangement-invariant space and let be the closure of the space of bounded functions in . Elements of orthogonal to , that is, elements , , such that for each , are investigated. The set of orthogonal elements is characterized in the case when is a Marcinkiewicz or an Orlicz space. If an Orlicz space is considered with the Luxemburg norm, then the set is the algebraic sum of and . Each nonseparable rearrangement-invariant space such that is shown to contain an asymptotically isometric copy of the space . Bibliography: 17 titles.
期刊介绍：
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in:
Mathematical analysis
Ordinary differential equations
Partial differential equations
Mathematical physics
Geometry
Algebra
Functional analysis
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