References
-
R. Bhatia and M. Uchiyama, The operator equation
${\sum_{i=0}^{n}A^{n-i}XB^i}$ = Y, Expo. Math., 27(2009), 251-255. https://doi.org/10.1016/j.exmath.2009.02.001 - N. Chan and M. Kwong, Hermitian matrix inequalities and a conjecture, Amer. Math. Monthly, 92(1985), 533-541. https://doi.org/10.2307/2323157
-
T. Furuta,
$A{\geq}B{\geq}0$ assures$(B^rA^pB^r)^{1/q}{\geq}B^{(p+2r)/q}\;for\;r{\geq}0,p{\geq}0,q{\geq}1\;with\;(1+2r)q{\geq}p+2r$ , Proc. Amer. Math. Soc., 101(1987), 85-88. -
T. Furuta, Positive semidefinite solution of the operator equation
${\sum_{j=1}^{n}A^{n-j}XA^{j-1}=B$ , Linear Alg. and Its Appl., 432(2010), 949-955. https://doi.org/10.1016/j.laa.2009.10.008 - M. Kwong, Some results on matrix monotone functions, Linear Alg. and Its Appl., 118(1989), 129-153. https://doi.org/10.1016/0024-3795(89)90577-6