{"title":"New Identities for Moore–Penrose Inverses of Some Operator Products and Their Reverse-order Laws","authors":"Mehdi Mohammadzadeh Karizaki, Javad Farokhi-Ostad","doi":"10.1007/s10114-023-1645-5","DOIUrl":null,"url":null,"abstract":"<div><p>We establish new identities for Moore–Penrose inverses of some operator products, and prove their associated reverse-order laws. Moreover, our results concerning the Moore–Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville’s inclusions are made into equalities.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-023-1645-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish new identities for Moore–Penrose inverses of some operator products, and prove their associated reverse-order laws. Moreover, our results concerning the Moore–Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville’s inclusions are made into equalities.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.