Abstract
The objective of this paper is to study the reverse order laws for the generalized Drazin inverse in a Banach algebra on the conditions of the commutativity up to a factor, generalizing recent results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baksalary, O.M., Trenkler, G.: Core inverse of matrices. Linear Multilinear Algebra 58(6), 681–697 (2010)
Deng, C.Y.: Reverse order law for the group inverses. J. Math. Anal. Appl. 382(2), 663–671 (2011)
Djordjević, D.S.: Unified approach to the reverse order rule for generalized inverses. Acta Sci. Math. (Szeged) 67, 761–776 (2001)
Drazin, M.P.: Pseudoinverse in associative rings and semigroups. Am. Math. Mon. 65, 506–514 (1958)
Greville, T.N.E.: Note on the generalized inverse of a matrix product. SIAM Rev. 8, 518–521 (1966)
Hartwig, R.E.: The reverse order law revisited. Linear Algebra Appl. 76, 241–246 (1986)
Koliha, J.J.: A generalized Drazin inverse. Glasg. Math. J. 38, 367–381 (1996)
Mary, X.: Reverse order law for the group inverse in semigroups and rings. Commun. Algebra 43, 2492–2508 (2015)
Mosić, D.: Reverse order laws for the generalized Drazin inverse in Banach algebras. J. Math. Anal. Appl. 429(1), 461–477 (2015)
Mosić, D., Djordjević, D.S.: Reverse order law for the group inverse in rings. Appl. Math. Comput. 219(5), 2526–2534 (2012)
Mosić, D., Djordjević, D.S.: Further results on the reverse order law for the group inverse in rings. Appl. Math. Comput. 219(19), 9971–9977 (2013)
Mosić, D., Djordjević, D.S.: The reverse order law \((ab)^\#=b^{\dagger } (a^{\dagger } abb^{\dagger })^{\dagger } a^{\dagger }\) in rings with involution. Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matemticas 109(2), 257–265 (2015)
Sun, W., Wei, Y.: Inverse order rule for weighted generalized inverse SIAM. J. Matrix Anal. Appl. 19, 772–775 (1998)
Tian, Y.: Using rank formulas to characterize equalities for Moore-Penrose inverses of matrix product. Appl. Math. Comput. 147, 581–600 (2004)
Wang, H., Liu, X.: Characterizations of the core inverse and the core partial ordering. Linear and Multilinear Algebra 63(9), 1829–1836 (2015)
Zhang, X.X., Xu, S.Z., Chen, J.L.: Core partial order in rings with involution (2016). arXiv:1601.03120 [math.RA]
Author information
Authors and Affiliations
Corresponding author
Additional information
The author is supported by the Ministry of Education and Science, Republic of Serbia, Grant No. 174007.
Rights and permissions
About this article
Cite this article
Mosić, D. Reverse order laws on the conditions of the commutativity up to a factor. RACSAM 111, 685–695 (2017). https://doi.org/10.1007/s13398-016-0319-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-016-0319-x