Jacobson's Lemma for Generalized Drazin–Riesz Inverses  

作　　者：Soufiane HADJI Hassane ZGUITTI 

机构地区：[1]Department of Mathematics,Dhar El Mahraz Faculty of Science,Sidi Mohamed Ben Abdellah University,P.O.Box 1796 Fes-Atlas,30003 Fez Morocco

出　　处：《Acta Mathematica Sinica,English Series》2023年第3期481-496,共16页数学学报（英文版）

摘　　要：For bounded linear operators A,B,C and D on a Banach space X,we show that if BAC=BDB and CDB=CAC then I-AC is generalized Drazin-Riesz invertible if and only if I-BD is generalized Drazin-Riesz invertible,which gives a positive answer to Question 4.9 in Yan,Zeng and Zhu[Complex Anal.Oper.Theory 14,Paper No.12(2020)].In particular,we show that Jacobson’s lemma holds for generalized Drazin-Riesz inverses.

关 键 词：Jacobson's lemma Drazin inverse generalized Drazin-Riesz inverse 

分 类 号：O177[理学—数学]