{"title":"关于严格奇异算子的注释","authors":"Ersin Kızgut, M. Yurdakul","doi":"10.12988/ijma.2017.77103","DOIUrl":null,"url":null,"abstract":"A continuous linear operator $T:E \\to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon $LB(E,F)=L_s(E,F)$, which means that every continuous linear bounded operator defined on $E$ into $F$ is strictly singular.","PeriodicalId":431531,"journal":{"name":"International Journal of Mathematical Analysis","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on strictly singular operators\",\"authors\":\"Ersin Kızgut, M. Yurdakul\",\"doi\":\"10.12988/ijma.2017.77103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A continuous linear operator $T:E \\\\to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon $LB(E,F)=L_s(E,F)$, which means that every continuous linear bounded operator defined on $E$ into $F$ is strictly singular.\",\"PeriodicalId\":431531,\"journal\":{\"name\":\"International Journal of Mathematical Analysis\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/ijma.2017.77103\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/ijma.2017.77103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A continuous linear operator $T:E \to F$ is called strictly singular if it cannot be invertible on any infinite dimensional closed subspace of its domain. In this note we discuss sufficient conditions and consequences of the phenomenon $LB(E,F)=L_s(E,F)$, which means that every continuous linear bounded operator defined on $E$ into $F$ is strictly singular.
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