Volume 36 • Number 3 • 2013   • Furuta Type Inequalities Dealing with Pedersen-Takesaki Type Operator Equations Jian Shi and Zongsheng Gao Abstract. In this paper, we study the existence of solutions of some Pedersen-Takesaki type operator equations via Furuta type inequalities. Firstly, we investigate characterizations of operator order $A\geqslant B$ and chaotic operator order log $A \geqslant$ log $B$ for positive definite operators $A$ and $B$ in terms of Pedersen-Takesaki type operator equations, which extend the related results before. Finally, we give some applications of complete form of Furuta inequality to Pedersen-Takesaki type operator equations and prove the related characterizations of the solutions. 2010 Mathematics Subject Classification: 47A63 Full text: PDF