# Positive Solutions of a Class of Operator Equations

### Abstract

Positive solutions of a class of matrix equations were studied by Bhatia, et al.,*Bull. London Math. Soc.*, 32, 214 (2000),

*SIAM J. Matrix Anal. Appl.*, 14, 132 (1993) and 27, 103–114 (2005), by Kwong,

*Linear Algebra Appl.*, 108, 177–197 (1988), and by Cvetkovi? and Milovanovi?, [

*Linear Algebra Appl.*, 429, 2401–2414 (2008)]. Following the idea used in the last paper, we study a class of operator equations in infinite-dimensional spaces and prove that the positivity of solutions can be established for this class of equations under the condition that a certain rational function is positive semidefinite.

Published

25.02.2015

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 67, no. 2, Feb. 2015, pp. 245-60, http://umj.imath.kiev.ua/index.php/umj/article/view/1977.

Issue

Section

Research articles