一些蕴含Furuta不等式的算子单调函数的算子不等式

摘要

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.%In this paper, we study the relations between the operator inequalities and the operator monotone functions. By using the fundamental conclusions based on majorization, namely, product lemma and product theorem for operator monotone functions, we can give some operator inequalities. This result contains the Furuta inequality, which has a huge impact on positive operator theory.