{"title":"扩展weyl型定理和摄动","authors":"M. Berkani, H. Zariouh","doi":"10.3318/PRIA.2010.110.1.73","DOIUrl":null,"url":null,"abstract":"In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"EXTENDED WEYL TYPE THEOREMS AND PERTURBATIONS\",\"authors\":\"M. Berkani, H. Zariouh\",\"doi\":\"10.3318/PRIA.2010.110.1.73\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"2 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2010.110.1.73\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2010.110.1.73","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In [9], we introduced the properties (b) and (gb), which are analogous of Browder and generalised Browder theorems. In this paper we study the stability of properties (b) and (gb) under commutative perturbations by finite rank, compact and nilpotent operators. Among other results, we prove that if T is an operator acting on a Banach space and possesses property (b) and N is a nilpotent operator commuting with T, then T + N possesses property (b). The same result holds for property (gb) in the case of a-polaroid operators.
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