Some Properties of Furuta Type Inequalities and Applications

الملخص EN

This work is to consider Furuta type inequalities and their applications.

Firstly, some Furuta type inequalities under A≥B≥0 are obtained via Loewner-Heinz inequality; as an application, a proof of Furuta inequality is given without using the invertibility of operators.

Secondly, we show a unified satellite theorem of grand Furuta inequality which is an extension of the results by Fujii et al.

At the end, a kind of Riccati type operator equation is discussed via Furuta type inequalities.