{"title":"Banach格上的DW-DP算子和dw -有限算子","authors":"Jin Xi Chen, Jingge Feng","doi":"10.1007/s43036-025-00429-x","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call <i>DW</i>-DP operators and <i>DW</i>-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that <i>DW</i>-DP (resp. <i>DW</i>-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak<span>\\(^*\\)</span> Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive <i>DW</i>-DP and positive <i>DW</i>-limited operators are given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00429-x.pdf","citationCount":"0","resultStr":"{\"title\":\"DW-DP operators and DW-limited operators on Banach lattices\",\"authors\":\"Jin Xi Chen, Jingge Feng\",\"doi\":\"10.1007/s43036-025-00429-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call <i>DW</i>-DP operators and <i>DW</i>-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that <i>DW</i>-DP (resp. <i>DW</i>-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak<span>\\\\(^*\\\\)</span> Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive <i>DW</i>-DP and positive <i>DW</i>-limited operators are given.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2025-03-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43036-025-00429-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-025-00429-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-025-00429-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
DW-DP operators and DW-limited operators on Banach lattices
This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call DW-DP operators and DW-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that DW-DP (resp. DW-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak\(^*\) Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive DW-DP and positive DW-limited operators are given.
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