Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (1): 1-9.

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Reverse Order Law of the Drazin Inverse for Bounded Linear Operators

Hua Wang1,*,Jinfeng Li1(),Junjie Huang2   

  1. 1 College of Sciences, Inner Mongolia University of Technology, Hohhot 010051
    2 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
  • Received:2018-10-05 Online:2020-01-26 Published:2020-04-08
  • Contact: Hua Wang E-mail:1677904349@qq.com; hjjwh@sina.com
  • Supported by:
    国家自然科学基金(11461049);国家自然科学基金(11601249);内蒙古自然科学基金(2018MS01002);内蒙古自然科学基金(2017MS0118)

Abstract:

In this paper, we discuss the Drazin invertibility and reverse order law of the Drazin inverse for the product of two bounded linear operators. Under the assumptions that P commutes with PQP and Q commutes with QPQ, respectively, we derive the Drazin invertibility of PQ and some equivalent conditions for the reverse order law (PQ)D=QDPD to hold by using space decomposition technique.

Key words: Reverse order law, Drazin inverse, Bounded linear operator

CLC Number: 

  • O151.21
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