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The Drazin inverse of the sum of two products

Safae Alaoui Chrifi|Abdelaziz Tajmouati
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회논문집 (Communications of the KMS)|제37권 제3호|pp. 705-718|DOI 10.4134/CKMS.c210040

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키워드

Drazin inverseadditive resultsbounded linear operatoroperator matrix
주제분류수학

초록

In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.

Abstract

In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.

참고문헌 (14)

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  9. Carl D. Meyer, Jr., "The Index and the Drazin Inverse of Block Triangular Matrices", SIAM Journal on Applied Mathematics, 33(1), pp.1~7 (1977), Society for Industrial & Applied Mathematics (SIAM)[DOI]
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  13. Huihui Zhu, "Additive and Product Properties of Drazin Inverses of Elements in a Ring", Bulletin of the Malaysian Mathematical Sciences Society, 40(1), pp.259~278 (2016), Springer Science and Business Media LLC[DOI]
  14. Guifen Zhuang, "Additive property of Drazin invertibility of elements in a ring", Linear and Multilinear Algebra, 60(8), pp.903~910 (2012), Informa UK Limited[DOI]

관련 논문AI추천

Group inverse and generalized Drazin inverse of block matrices in a Banach algebraDijana Mosic대한수학회 · 대한수학회보2014 · 제51권 제3호REPRESENTATION OF BOUNDED LINEAR OPERATORS WITH EQUAL SPECTRAL PROJECTIONS AT ZERODong-Jun Chen, Yun Zhang대한수학회 · 대한수학회논문집2010 · 제25권 제4호Weighted gDMP inverse of operators between Hilbert spacesDijana Mosic대한수학회 · 대한수학회보2018 · 제55권 제4호The G-Drazin Inverse of an Operator Matrix over Banach SpacesFarzaneh Tayebi, Marjan Sheibani Abdolyousefi, Nahid Ashrafi, Rahman Bahmani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2024 · 제64권 제2호Representations of the Moore-Penrose inverse of 2×2 block operator valued matricesChun Yuan Deng, Hong Ke Du대한수학회 · 대한수학회지2009 · 제46권 제6호Characterizations and the Moore-Penrose inverse of hypergeneralized k-projectorsMarina Tosic대한수학회 · 대한수학회보2014 · 제51권 제2호

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