Furuta type inequalities dealing with Pedersen-Takesaki type operator equations

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?B and chaotic operator order log A ? 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.