owner-Heinz inequality;operator equation;Lyapunov equation;positive semidefinite solution;"/> owner-Heinz inequality;operator equation;Lyapunov equation;positive semidefinite solution;"/> An Application of Furuta Inequality to Linear Operator Equations | Korea Science
JOURNAL BROWSE
Search
Advanced SearchSearch Tips
An Application of Furuta Inequality to Linear Operator Equations
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 4,  2009, pp.743-750
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.4.743
 Title & Authors
An Application of Furuta Inequality to Linear Operator Equations
Ahn, Eun-Kyung; Lim, Yong-Do;
  PDF(new window)
 Abstract
A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation for a fixed positive definite operator A is given via the Furuta inequality.
 Keywords
Furuta inequality;Lowner-Heinz inequality;operator equation;Lyapunov equation;positive semidefinite solution;
 Language
English
 Cited by
 References
1.
R. Bhatia and M. Uchiyama, The operator equation ${\sum_{i=0}^{n}A^{n-i}XB^i}$ = Y, Expo. Math., 27(2009), 251-255. crossref(new window)

2.
N. Chan and M. Kwong, Hermitian matrix inequalities and a conjecture, Amer. Math. Monthly, 92(1985), 533-541. crossref(new window)

3.
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.

4.
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. crossref(new window)

5.
M. Kwong, Some results on matrix monotone functions, Linear Alg. and Its Appl., 118(1989), 129-153. crossref(new window)