## Some properties of Furuta type inequalities and applications.(English)Zbl 1472.47015

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 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.

### MSC:

 47A63 Linear operator inequalities 47A62 Equations involving linear operators, with operator unknowns

Zbl 1270.47016
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### References:

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