{"title":"集体阶收敛和集体合格算子集","authors":"Eduard Emelyanov","doi":"arxiv-2408.03671","DOIUrl":null,"url":null,"abstract":"Collective versions of order convergences and corresponding types of\ncollectively qualified sets of operators in vector lattices are investigated.\nIt is proved that every collectively order continuous set of operators between\nArchimedean vector lattices is collectively order bounded.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"84 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Collective order convergence and collectively qualified set of operators\",\"authors\":\"Eduard Emelyanov\",\"doi\":\"arxiv-2408.03671\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Collective versions of order convergences and corresponding types of\\ncollectively qualified sets of operators in vector lattices are investigated.\\nIt is proved that every collectively order continuous set of operators between\\nArchimedean vector lattices is collectively order bounded.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"84 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.03671\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.03671","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Collective order convergence and collectively qualified set of operators
Collective versions of order convergences and corresponding types of
collectively qualified sets of operators in vector lattices are investigated.
It is proved that every collectively order continuous set of operators between
Archimedean vector lattices is collectively order bounded.
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