{"title":"Riesz空间中的Cantor-Bernstein型定理","authors":"Marek Wójtowicz","doi":"10.1016/1385-7258(88)90011-X","DOIUrl":null,"url":null,"abstract":"<div><p>We generalize the main result of [21] to Riesz spaces. Let <em>X</em> and <em>Y</em> be Riesz spaces with σ-complete Boolean algebras of projection bands. If <em>X</em> and <em>Y</em> are each Riesz isomorphic to a projection band of the other space then the spaces are Riesz isomorphic. As an application of the above theorem we give an example of non-Riesz isomorphic Banach lattices such that: (1) their order (= topological) duals are Riesz isomorphic and (2) each of them is Riesz isomorphic to a projection band of the other one.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 93-100"},"PeriodicalIF":0.0000,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90011-X","citationCount":"9","resultStr":"{\"title\":\"On Cantor-Bernstein type theorems in Riesz spaces\",\"authors\":\"Marek Wójtowicz\",\"doi\":\"10.1016/1385-7258(88)90011-X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We generalize the main result of [21] to Riesz spaces. Let <em>X</em> and <em>Y</em> be Riesz spaces with σ-complete Boolean algebras of projection bands. If <em>X</em> and <em>Y</em> are each Riesz isomorphic to a projection band of the other space then the spaces are Riesz isomorphic. As an application of the above theorem we give an example of non-Riesz isomorphic Banach lattices such that: (1) their order (= topological) duals are Riesz isomorphic and (2) each of them is Riesz isomorphic to a projection band of the other one.</p></div>\",\"PeriodicalId\":100664,\"journal\":{\"name\":\"Indagationes Mathematicae (Proceedings)\",\"volume\":\"91 1\",\"pages\":\"Pages 93-100\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1988-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/1385-7258(88)90011-X\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indagationes Mathematicae (Proceedings)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/138572588890011X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/138572588890011X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We generalize the main result of [21] to Riesz spaces. Let X and Y be Riesz spaces with σ-complete Boolean algebras of projection bands. If X and Y are each Riesz isomorphic to a projection band of the other space then the spaces are Riesz isomorphic. As an application of the above theorem we give an example of non-Riesz isomorphic Banach lattices such that: (1) their order (= topological) duals are Riesz isomorphic and (2) each of them is Riesz isomorphic to a projection band of the other one.
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