Operator inequalities dealing with operator equations

Details Operator inequalities dealing with operator equations Operator inequalities dealing with operator equations

2011-08-15

arxiv.org/abs/1108.3009v1

Mathematics

Functional Analysis

Scientific paper

In this paper, we study the existence of solutions of some kinds of operator equations via operator inequalities. First, we investigate characterizations of operator order $A\geqslant B >0$ and chaotic operator order log $A \geqslant$ log $B$ for positive definite operators $A$, $B$ in terms of operator equations, and generalize the results in \cite{CSLin}. Then, we introduce applications of complete form of Furuta inequality in operator equations. Some kinds of operator equations are researched and related characterizations of solutions are proved.

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