Xiao ZHANG
,
Guoxing JI
. SOLUTIONS TO THE SYSTEM OF OPERATOR EQUATIONS AXB=C=BXA[J]. Acta mathematica scientia, Series B, 2018
, 38(4)
: 1143
-1150
.
DOI: 10.1016/S0252-9602(18)30804-X
[1] Arias M L, Gonzalez M C. Positive solutions to operator equations AXB=C. Linear Algebra Appl, 2010, 433(6):1194-1202
[2] Douglas R G. On majorization, factorization and range inclusion of operators in Hilbert space. Proc Amer Math Soc, 1966, 17(2):413-415
[3] Cvetković D S. Re-nnd solutions of the matrix equation AXB=C. J Aust Math Soc, 2008, 84(1):63-72
[4] Deng C. On the solutions of operator equation CAX=C=XAC. J Math Anal Appl, 2013, 398(2):664-670
[5] Don F J. Henk. On the symmetric solutions of a linear matrix equation. Linear Algebra Appl, 1987, 93:1-7
[6] Wang Q W, Wu Z C. Common hermitian solutions to some operator equations on Hilbert C*-modules. Linear Algebra Appl, 2010, 432(12):3159-3171
[7] Xu Q, Sheng L, Gu Y. The solutions to some operator equation. Linear Algebra Appl, 2008, 429:1997-2024
[8] Xu Q. Common hermitian and positive solutions to the adjointable operator equations AX=C, XB=D. Linear Algebra Appl, 2008, 429(1):1-11
[9] Lu T. Some nonlinear operator equations and their approximate solutions. Acta Mathematica Scientia, 1982, 2(4):421-435
[10] Dajić A, Koliha J J. Positive solutions to the equations AX=C, XB=D for Hilbert space operators. J Math Anal Appl, 2007, 333(2):567-576
[11] Vosough M, Moslehian M S. Solutions of the system of operator equations AXB=B=BXA via *-order. Electronic J Linear Algabra, 2017, 32:172-183
[12] Nashed M Z. Inner, outer, and generalized inverses in Banach and Hilbert spaces. Numer Funct Anal Optim, 1987, 9(3/4):261-325
[13] Xu X M, Du H K, Fang X C. The supremum of linear operators for the *-order. Linear Algebra Appl, 2010, 433(11):2198-2207
[14] Khatri C G, Mitra S K. Hermitian and nonnegative definite solutions of linear matrix equations. SIAM J Appl Math, 1976, 31(4):579-585
[15] Yan K, Fang X C. Common properties of the operator products in spectral theory. Ann Funct Anal, 2015, 6:60-69