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http://dx.doi.org/10.4134/JKMS.2008.45.5.1417

THE SOLUTIONS OF SOME OPERATOR EQUATIONS  

Cvetkovic-Ilic, Dragana S. (Department of Mathematics Faculty of Sciences and Mathematics University of Nis)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.5, 2008 , pp. 1417-1425 More about this Journal
Abstract
In this paper we consider the solvability and describe the set of the solutions of the operator equations $AX+X^{*}C=B$ and $AXB+B^{*}X^{*}A^{*}=C$. This generalizes the results of D. S. Djordjevic [Explicit solution of the operator equation $A^{*}X+X^{*}$A=B, J. Comput. Appl. Math. 200(2007), 701-704].
Keywords
operator equation; Moore-Penrose inverse; g-invertibility;
Citations & Related Records

Times Cited By Web Of Science : 4  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
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1 A. Ben-Israel and T. N. E. Greville, Generalized Inverses, Theory and applications. Second edition. CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 15. Springer-Verlag, New York, 2003
2 Y. X. Peng, X. Y. Hu, and L. Zhang, An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C, Appl. Math. Comput. 160 (2005), no. 3, 763-777   DOI   ScienceOn
3 S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Corrected reprint of the 1979 original. Dover Publications, Inc., New York, 1991
4 S. R. Caradus, Generalized Inverses and Operator Theory, Queen's Papers in Pure and Applied Mathematics, 50. Queen's University, Kingston, Ont., 1978
5 G. Kitagawa, An algorithm for solving the matrix equation X = FX$F^{T}$ + S , International Journal of Control, 25 (1977), no. 5, 745-753   DOI   ScienceOn
6 D. S. Djordjevic, Explicit solution of the operator equation $A^{*}$X+$X^{*}$A = B, J. Comput. Appl. Math. 200 (2007), no. 2, 701-704   DOI   ScienceOn
7 R. E. Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, 109. Marcel Dekker, Inc., New York, 1988
8 P. Kirrinnis, Fast algorithms for the Sylvester equation AX - X$B^{T}$= C, Theoret. Comput. Sci. 259 (2001), no. 1-2, 623-638   DOI   ScienceOn
9 Z. Y. Peng and X. Y. Hu, The reflexive and anti-reflexive solutions of the matrix equation AX = B, Linear Algebra Appl. 375 (2003), 147-155   DOI   ScienceOn
10 D. C. Sorensen and A. C. Antoulas, The Sylvester equation and approximate balanced reduction, Linear Algebra Appl. 351/352 (2002), 671-700