Algebraic properties of generalized inverse of operators
DOI:
https://doi.org/10.5269/bspm.78820Resumo
This study explores the algebraic properties of Moore-Penrose inverse, Drazin-Moore-Penrose inverse, and the dual Drazin-Moore-Penrose inverse of operators defined on Hilbert spaces. It presents some sufficient conditions under which reverse order law, forward order law and absorption law hold, utilizing various types of generalized inverses.
Referências
1. Djordjevic, D. S., Dincic, N.C., Reverse order law for the Moore-Penrose inverse, J. Math. Anal. Appl., 361(1), 252-261, (2010).
2. Du, H. K., Deng, C. Y., The representation and characterization of Drazin inverses of operators on a Hilbert space, Linear Algebra Appl, 407(15), 117-124, (2005).
3. Jin, H., Benitez, J., The absorption laws for the generalized inverses in rings, Electron. J. Linear Algebra, 30, 827-842, (2015).
4. Bouldin, R.H., The pseudo-inverse of a product, SIAM J. Appl. Math., 25, 489–495, (1973).
5. Izumino, S., The product of operators with closed range and an extension of the reverse order law, Tohoku Math. J., 34, 43–52, (1982).
6. Greville, T.N.E., Note on the generalized inverse of a matrix product, SIAM Rev., 8, 518–521, (1966).
7. Wang, X., Yu, A., Li, T., Deng, C., Reverse order laws for the Drazin inverses, Journal of Mathematical Analysis and Applications, 444(1), 672-689, (2016).
8. Tian, Y., Using rank formulas to characterize equalities for Moore–Penrose inverses of matrix products, Appl. Math. Comput., 147, 581–600, (2004).
9. Gao, Y., Chen, J., Wang, L., Zou, H., Absorption laws and reverse order laws for generalized core inverses, Commun. Algebra, 49, 3241-3254, (2015).
10. Yu, A., Deng, C., Characterizations of DMP inverse in a Hilbert space, Calcolo, 53(3), 331-341, (2016).
2. Du, H. K., Deng, C. Y., The representation and characterization of Drazin inverses of operators on a Hilbert space, Linear Algebra Appl, 407(15), 117-124, (2005).
3. Jin, H., Benitez, J., The absorption laws for the generalized inverses in rings, Electron. J. Linear Algebra, 30, 827-842, (2015).
4. Bouldin, R.H., The pseudo-inverse of a product, SIAM J. Appl. Math., 25, 489–495, (1973).
5. Izumino, S., The product of operators with closed range and an extension of the reverse order law, Tohoku Math. J., 34, 43–52, (1982).
6. Greville, T.N.E., Note on the generalized inverse of a matrix product, SIAM Rev., 8, 518–521, (1966).
7. Wang, X., Yu, A., Li, T., Deng, C., Reverse order laws for the Drazin inverses, Journal of Mathematical Analysis and Applications, 444(1), 672-689, (2016).
8. Tian, Y., Using rank formulas to characterize equalities for Moore–Penrose inverses of matrix products, Appl. Math. Comput., 147, 581–600, (2004).
9. Gao, Y., Chen, J., Wang, L., Zou, H., Absorption laws and reverse order laws for generalized core inverses, Commun. Algebra, 49, 3241-3254, (2015).
10. Yu, A., Deng, C., Characterizations of DMP inverse in a Hilbert space, Calcolo, 53(3), 331-341, (2016).
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Publicado
2025-09-30
Edição
Seção
Conf. Issue: Advances in Nonlinear Analysis and Applications
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