{"title":"性质(gt)在摄动和张量积作用下的稳定性","authors":"M. Rashid, M. Chō","doi":"10.7153/oam-2023-17-19","DOIUrl":null,"url":null,"abstract":". An operator T acting on a Banach space X obeys property ( gt ) if the isolated points of the spectrum ( T ) of T which are eigenvalues are exactly those points of the spectrum for which T − is an upper semi-B -Fredholm with index less than or equal to 0. In this paper we study the stability of property ( gt ) under perturbations by fi nite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T . Moreover, we study the transfer of property ( gt ) from a bounded linear operator T acting on a Banach space X and a bounded linear operator S acting on a Banach space Y to their tensor product T ⊗ S . Mathematics","PeriodicalId":56274,"journal":{"name":"Operators and Matrices","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The stability of property (gt) under perturbation and tensor product\",\"authors\":\"M. Rashid, M. Chō\",\"doi\":\"10.7153/oam-2023-17-19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". An operator T acting on a Banach space X obeys property ( gt ) if the isolated points of the spectrum ( T ) of T which are eigenvalues are exactly those points of the spectrum for which T − is an upper semi-B -Fredholm with index less than or equal to 0. In this paper we study the stability of property ( gt ) under perturbations by fi nite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T . Moreover, we study the transfer of property ( gt ) from a bounded linear operator T acting on a Banach space X and a bounded linear operator S acting on a Banach space Y to their tensor product T ⊗ S . Mathematics\",\"PeriodicalId\":56274,\"journal\":{\"name\":\"Operators and Matrices\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Operators and Matrices\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7153/oam-2023-17-19\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operators and Matrices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/oam-2023-17-19","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The stability of property (gt) under perturbation and tensor product
. An operator T acting on a Banach space X obeys property ( gt ) if the isolated points of the spectrum ( T ) of T which are eigenvalues are exactly those points of the spectrum for which T − is an upper semi-B -Fredholm with index less than or equal to 0. In this paper we study the stability of property ( gt ) under perturbations by fi nite rank operators, by nilpotent operators and, more generally, by algebraic operators commuting with T . Moreover, we study the transfer of property ( gt ) from a bounded linear operator T acting on a Banach space X and a bounded linear operator S acting on a Banach space Y to their tensor product T ⊗ S . Mathematics
期刊介绍:
''Operators and Matrices'' (''OaM'') aims towards developing a high standard international journal which will publish top quality research and expository papers in matrix and operator theory and their applications. The journal will publish mainly pure mathematics, but occasionally papers of a more applied nature could be accepted. ''OaM'' will also publish relevant book reviews.
''OaM'' is published quarterly, in March, June, September and December.