Wg-Drazin-star operator and its dual

References

[1] Ben-Israel, A.—Greville, T. N. E.: Generalized inverses: theory and applications, 2nd ed., Springer, New York, 2003.Search in Google Scholar

[2] Castro González, N.—Koliha, J. J.: New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), 1085–1097.Search in Google Scholar

[3] Catral, M.—Olesky, D. D.—Van Den Driessche, P.: Block representations of the Drazin inverse of a bipartite matrix, Electron. J. Linear Algebra 18 (2009), 98–107.Search in Google Scholar

[4] Cline, R. E.—Greville, T. N. E.: A Drazin inverse for rectangular matrices, Linear Algebra Appl. 29 (1980), 53–62.Search in Google Scholar

[5] Dajić, A.—Koliha, J. J.: The weighted g–Drazin inverse for operators, J. Australian Math. Soc. 82 (2007), 163–181.Search in Google Scholar

[6] Dolinar, G.—Kuzma, B.—Marovt, J.—Ungor, B.: On some partial orders on a certain subset of the power set of rings, Glasnik Matematički 55(75) (2020), 177–190.Search in Google Scholar

[7] Dolinar, G.—Halicioglu, S.—Kuzma, B.—Marovt, J.—Ungor, B.: Preservers of the left-star and right-star partial orders, Linear Algebra Appl. 587 (2020), 70–91.Search in Google Scholar

[8] Douglas, R. G.: On majorization, factorization and range inclusion of operators in Hilbert spaces, Proc. Amer. Math. Soc. 17 (1966), 413–416.Search in Google Scholar

[9] Drazin, M. P.: Pseudo-inverses in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514.Search in Google Scholar

[10] Ferreyra, D. E.—Levis, F. E.—Thome, N.: Maximal classes of matrices determining generalized inverses, Appl. Math. Comput. 333 (2018), 42–52.Search in Google Scholar

[11] He, Z.: Some new results on a system of Sylvester-type quaternion matrix equations, Linear Multilinear Algebra 69(16) (2021), 3069–3091.Search in Google Scholar

[12] Koliha, J. J.: A generalized Drazin inverse, Glasgow Math. J. 38 (1996), 367–381.Search in Google Scholar

[13] Kyrchei, I. I.: Determinantal representations of the core inverse and its generalizations with applications, J. Math. 2019 (2019), Art. ID 1631979.Search in Google Scholar

[14] Kyrchei, I. I.: Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses, J. Math. 2020 (2020), Art. ID 9816038.Search in Google Scholar

[15] Liu, X.—Cai, N.: High-order iterative methods for the DMP inverse, J. Math. 2018 (2018), Art. ID 8175935.Search in Google Scholar

[16] Ma, H.—Gao, X.—Stanimirović, P. S.: Characterizations, iterative method, sign pattern and perturbation analysis for the DMP inverse with its applications, Appl. Math. Comput. 378 (2020), Art. ID 125196.Search in Google Scholar

[17] Malik, S. B.—Thome, N.: On a new generalized inverse for matrices of an arbitrary index, Appl. Math. Comput. 226 (2014), 575–580.Search in Google Scholar

[18] Marovt, J.: Orders in rings based on the core-nilpotent decomposition, Linear Multilinear Algebra 66(4) (2018), 803–820.Search in Google Scholar

[19] Meng, L. S.: The DMP inverse for rectangular matrices, Filomat 31(19) (2017), 6015–6019.Search in Google Scholar

[20] Mosić, D.: Drazin-star and star-Drazin matrices, Results Math. 75(61) (2020), Art. No. 61.Search in Google Scholar

[21] Mosić, D.: Maximal classes of operators determining some weighted generalized inverses, Linear Multilinear Algebra 68(11) (2020), 2201–2220.Search in Google Scholar

[22] Mosić, D.: The Drazin inverse of the sum of two matrices, Math. Slovaca 68 (2018), 767–772.Search in Google Scholar

[23] Mosić, D.: Weighted core–EP inverse of an operator between Hilbert spaces, Linear Multilinear Algebra 67(2) (2019), 278–298.Search in Google Scholar

[24] Mosić, D.: Weighted gDMP inverse of operators between Hilbert spaces, Bull. Korean Math. Soc. 55(4) (2018), 1263–1271.Search in Google Scholar

[25] Mosić, D.—Djordjević, D. S.: The gDMP inverse of Hilbert space operators, J. Spectr. Theory 8(2) (2018), 555–573.Search in Google Scholar

[26] Müller, V.: Spectral Theory of Linear Operators and Spectral System in Banach Algebras. Oper. Theor. Adv. Appl. 139, Birkhäuser Verlag, Basel, 2003.Search in Google Scholar

[27] Stanimirović, P. S.—Katsikis, V. N.—Ma, H.: Representations and properties of the W-weighted Drazin inverse, Linear Multilinear Algebra 65(6) (2017), 1080–1096.Search in Google Scholar

[28] Wei, Y.—Stanimirović, P. S.—Petković, M.: Numerical and Symbolic Computations of Generalized Inverses, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2018.Search in Google Scholar

[29] Yu, A.—Deng, C.: Characterizations of DMP inverse in a Hilbert space, Calcolo 53(3) (2016), 331–341.Search in Google Scholar

[30] Zhou, M.—Chen, J.: Integral representations of two generalized core inverses, Appl. Math. Comput. 333 (2018), 187–193.Search in Google Scholar

[31] Zhou, M.—Chen, J.—Thome, N.: The W-weighted Drazin-star matrix and its dual, Electronic J. Linear Algebra 37 (2021), 72–87.Search in Google Scholar

[32] Zhu, H.: On DMP inverses and m-EP elements in rings, Linear Multilinear Algebra 67(4) (2019), 756–766.Search in Google Scholar