منابع مشابه
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 ...
متن کاملFuruta 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 ...
متن کاملAn 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.
متن کاملA linear differential flatness approach to controlling the Furuta pendulum
The aim of this work is to motivate the use of linear flatness, or controllability, to design a feedback control law for the rather challenging mechanism known as the ‘Furuta pendulum’. This is achieved by introducing three feedback controller design options for the stabilization and rest-to-rest trajectory tracking tasks: a direct pole placement approach, a hierarchical high-gain approach and ...
متن کاملSome Complements of Cauchy’s Inequality on Time Scales
To unify the theory of continuous and discrete dynamic systems, in 1990 Hilger [16] proposed the study of dynamic systems on a time scale and developed the calculus for functions on a time scale (i.e., any closed subset of reals). The purpose of this paper is to establish some complements of Cauchy’s inequality on time scales, which extend some results of Cargo [6], Diaz, Goldman, and Metcalf [...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1994
ISSN: 0386-2194
DOI: 10.3792/pjaa.70.239