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http://dx.doi.org/10.4134/CKMS.c210040

THE DRAZIN INVERSE OF THE SUM OF TWO PRODUCTS  

Chrifi, Safae Alaoui (Sidi Mohamed Ben Abdellah University Faculty of Sciences Dhar Al Mahraz Laboratory of Mathematical Sciences and Applications (LASMA))
Tajmouati, Abdelaziz (Sidi Mohamed Ben Abdellah University Faculty of Sciences Dhar Al Mahraz Laboratory of Mathematical Sciences and Applications (LASMA))
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 705-718 More about this Journal
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.
Keywords
Drazin inverse; additive results; bounded linear operator; operator matrix;
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1 J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), no. 3, 367-381. https://doi.org/10.1017/S0017089500031803   DOI
2 P. Aiena and S. Triolo, Fredholm spectra and Weyl type theorems for Drazin invertible operators, Mediterr. J. Math. 13 (2016), no. 6, 4385-4400. https://doi.org/10.1007/s00009-016-0751-3   DOI
3 N. Castro-Gonzalez, E. Dopazo, and M. F. Martinez-Serrano, On the Drazin inverse of the sum of two operators and its application to operator matrices, J. Math. Anal. Appl. 350 (2009), no. 1, 207-215. https://doi.org/10.1016/j.jmaa.2008.09.035   DOI
4 S. A. Chrifi and A. Tajmouati, Triple reverse order law of drazin inverse for bounded linear operators, Filomat 354 (2021), no. 1, 147-155. https://doi.org/10.2298/FIL2101147A   DOI
5 D. S. Cvetkovic Ilic and Y. Wei, Algebraic properties of generalized inverses, Developments in Mathematics, 52, Springer, Singapore, 2017. https://doi.org/10.1007/978-981-10-6349-7   DOI
6 C. Deng and Y. Wei, New additive results for the generalized Drazin inverse, J. Math. Anal. Appl. 370 (2010), no. 2, 313-321. https://doi.org/10.1016/j.jmaa.2010.05.010   DOI
7 M. P. Drazin, Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506-514. https://doi.org/10.2307/2308576   DOI
8 R. E. Hartwig, G. Wang, and Y. Wei, Some additive results on Drazin inverse, Linear Algebra Appl. 322 (2001), no. 1-3, 207-217. https://doi.org/10.1016/S0024-3795(00)00257-3   DOI
9 H. Zhu and J. Chen, Additive and product properties of Drazin inverses of elements in a ring, Bull. Malays. Math. Sci. Soc. 40 (2017), no. 1, 259-278. https://doi.org/10.1007/s40840-016-0318-2   DOI
10 G. Zhuang, J. Chen, D. S. Cvetkovic-Ilic, and Y. Wei, Additive property of Drazin invertibility of elements in a ring, Linear Multilinear Algebra 60 (2012), no. 8, 903-910. https://doi.org/10.1080/03081087.2011.629998   DOI
11 X. Wang, A. Yu, T. Li, and C. Deng, Reverse order laws for the Drazin inverses, J. Math. Anal. Appl. 444 (2016), no. 1, 672-689. https://doi.org/10.1016/j.jmaa.2016.06.026   DOI
12 C. D. Meyer, Jr., and N. J. Rose, The index and the Drazin inverse of block triangular matrices, SIAM J. Appl. Math. 33 (1977), no. 1, 1-7. https://doi.org/10.1137/0133001   DOI
13 P. Patricio and R. E. Hartwig, Some additive results on Drazin inverses, Appl. Math. Comput. 215 (2009), no. 2, 530-538. https://doi.org/10.1016/j.amc.2009.05.021   DOI
14 H. Wang and J. Huang, Reverse order law for the Drazin inverse in Banach spaces, Bull. Iranian Math. Soc. 45 (2019), no. 5, 1443-1456. https://doi.org/10.1007/s41980-019-00207-5   DOI