{"title":"Banach代数中的伪Drazin逆","authors":"Jianlong Chen","doi":"10.4208/cmr.2021-0013","DOIUrl":null,"url":null,"abstract":"Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if and only if a+ J is Drazin invertible in A /J. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in A . We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order. AMS subject classifications: 15A09, 16U90, 46H05","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"The Pseudo Drazin inverses in Banach Algebras\",\"authors\":\"Jianlong Chen\",\"doi\":\"10.4208/cmr.2021-0013\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if and only if a+ J is Drazin invertible in A /J. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in A . We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order. AMS subject classifications: 15A09, 16U90, 46H05\",\"PeriodicalId\":66427,\"journal\":{\"name\":\"数学研究通讯\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究通讯\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4208/cmr.2021-0013\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2021-0013","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let A be a complex Banach algebra and J be the Jacobson radical of A . (1) We firstly show that a is generalized Drazin invertible in A if and only if a+ J is generalized Drazin invertible in A /J. Then we prove that a is pseudo Drazin invertible in A if and only if a+ J is Drazin invertible in A /J. As its application, the pseudo Drazin invertibility of elements in a Banach algebra is explored. (2) The pseudo Drazin order is introduced in A . We give the necessary and sufficient conditions under which elements in A have pseudo Drazin order, then we prove that the pseudo Drazin order is a pre-order. AMS subject classifications: 15A09, 16U90, 46H05