{"title":"Toeplitz代数的本质交换子及其性质","authors":"R. Hagger","doi":"10.7900/jot.2020feb06.2268","DOIUrl":null,"url":null,"abstract":"We study the Toeplitz algebra which is generated by Toeplitz operators with bounded symbols on the Fock space Fpα. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For p=2 these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for p≠2. Instead, we use a recent result of Fulsche to generalize Xia's theorems.","PeriodicalId":50104,"journal":{"name":"Journal of Operator Theory","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Essential commutants and characterizations of the Toeplitz algebra\",\"authors\":\"R. Hagger\",\"doi\":\"10.7900/jot.2020feb06.2268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the Toeplitz algebra which is generated by Toeplitz operators with bounded symbols on the Fock space Fpα. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For p=2 these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for p≠2. Instead, we use a recent result of Fulsche to generalize Xia's theorems.\",\"PeriodicalId\":50104,\"journal\":{\"name\":\"Journal of Operator Theory\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7900/jot.2020feb06.2268\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7900/jot.2020feb06.2268","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Essential commutants and characterizations of the Toeplitz algebra
We study the Toeplitz algebra which is generated by Toeplitz operators with bounded symbols on the Fock space Fpα. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated, sufficiently localized and weakly localized operators, respectively. Moreover, we determine its essential commutant and its essential bicommutant. For p=2 these results were obtained recently by Xia. However, Xia's ideas are mostly connected to Hilbert space theory and methods which are not applicable for p≠2. Instead, we use a recent result of Fulsche to generalize Xia's theorems.
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The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.
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