THE SOLUTIONS OF SOME OPERATOR EQUATIONS

Title & Authors
THE SOLUTIONS OF SOME OPERATOR EQUATIONS
Cvetkovic-Ilic, Dragana S.;

Abstract
In this paper we consider the solvability and describe the set of the solutions of the operator equations $\small{AX+X^{*}C=B}$ and $\small{AXB+B^{*}X^{*}A^{*}=C}$. This generalizes the results of D. S. Djordjevic [Explicit solution of the operator equation $\small{A^{*}X+X^{*}}$A=B
Keywords
operator equation;Moore-Penrose inverse;g-invertibility;
Language
English
Cited by
1.
ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD = E,Dehghan, Mehdi;Hajarian, Masoud;

대한수학회보, 2009. vol.46. 3, pp.511-519
1.
Maximization and minimization of the rank and inertia of the Hermitian matrix expression A-BX-(BX)* with applications, Linear Algebra and its Applications, 2011, 434, 10, 2109
References
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.
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

3.
S. R. Caradus, Generalized Inverses and Operator Theory, Queen's Papers in Pure and Applied Mathematics, 50. Queen's University, Kingston, Ont., 1978

4.
D. S. Djordjevic, Explicit solution of the operator equation \$A^{*}\$X+\$X^{*}\$A = B, J. Comput. Appl. Math. 200 (2007), no. 2, 701-704

5.
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

6.
P. Kirrinnis, Fast algorithms for the Sylvester equation AX - X\$B^{T}\$= C, Theoret. Comput. Sci. 259 (2001), no. 1-2, 623-638

7.
G. Kitagawa, An algorithm for solving the matrix equation X = FX\$F^{T}\$ + S , International Journal of Control, 25 (1977), no. 5, 745-753

8.
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

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

10.
D. C. Sorensen and A. C. Antoulas, The Sylvester equation and approximate balanced reduction, Linear Algebra Appl. 351/352 (2002), 671-700