A decreasing operator function associated with the Furuta inequality

Complete Form of Furuta Inequality

Let A and B be bounded linear operators on a Hilbert space satisfying A ≥ B ≥ 0. The well-known Furuta inequality is given as follows: Let r ≥ 0 and p > 0; then A r 2 Amin{1,p}A r 2 ≥ (A r 2 BpA r 2 ) min{1,p}+r p+r . In order to give a self-contained proof of it, Furuta (1989) proved that if 1 ≥ r ≥ 0, p > p0 > 0 and 2p0 + r ≥ p > p0, then (A r 2 Bp0A r 2 ) p+r p0+r ≥ (A r 2 BpA r 2 ) p+r p+r ...

An application of grand Furuta inequality to a type of operator equation

The existence of positive semidefinite solutions of the operator equation n ∑ j=1 AXA = Y is investigated by applying grand Furuta inequality. If there exists positive semidefinite solutions of the operator equation, one of the special types of Y is obtained, which extends the related result before. Finally, an example is given based on our result.

Furuta Inequality and Its Related Topics

This article is devoted to a brief survey of Furuta inequality and its related topics. It consists of 4 sections: 1. From Löwner-Heinz inequality to Furuta inequality, 2. Ando–Hiai inequality, 3. Grand Furuta inequality, and 4. Chaotic order. 1. From Löwner-Heinz inequality to Furuta inequality. The noncommutativity of operators appears in the fact that t is not orderpreserving. That is, there ...

An Operator Extension of Bohr's inequality

Differential subordination and superordination results associated with the Wright function

An operator associated with the Wright function is introduced in the open unit disk. Differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. In particular, some inequalities for modified Bessel functions are also obtained.