Some properties of Furuta type inequalities and applications (Q1724155)

Summary: This work is to consider Furuta type inequalities and their applications. Firstly, some Furuta-type inequalities under \(A \geq B \geq 0\) 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 \textit{M. Fujii} et al. [Linear Algebra Appl. 438, No. 4, 1580--1586 (2013; Zbl 1270.47016)]. At the end, a kind of Riccati-type operator equation is discussed via Furuta type inequalities.