{"title":"任意向量空间子空间的原子格及相关算子代数","authors":"D. Hadwin, K. Harrison","doi":"10.7153/oam-2022-16-73","DOIUrl":null,"url":null,"abstract":". We study a class of completely distributive, commutative, lattices of subspaces of an arbitrary vector space, and associated operator algebras. Our results are compared with corresponding results for commutative lattices of closed subspaces of a Hilbert space and associated algebras of bounded linear operators.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Atomic lattices of subspaces of an arbitrary vector space and associated operator algebras\",\"authors\":\"D. Hadwin, K. Harrison\",\"doi\":\"10.7153/oam-2022-16-73\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We study a class of completely distributive, commutative, lattices of subspaces of an arbitrary vector space, and associated operator algebras. Our results are compared with corresponding results for commutative lattices of closed subspaces of a Hilbert space and associated algebras of bounded linear operators.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7153/oam-2022-16-73\",\"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://doi.org/10.7153/oam-2022-16-73","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Atomic lattices of subspaces of an arbitrary vector space and associated operator algebras
. We study a class of completely distributive, commutative, lattices of subspaces of an arbitrary vector space, and associated operator algebras. Our results are compared with corresponding results for commutative lattices of closed subspaces of a Hilbert space and associated algebras of bounded linear operators.
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