论文标题
从积极到增生矩阵
From positive to accretive matrices
论文作者
论文摘要
本文的主要目的是讨论在更一般环境中积累矩阵的最新进步。特别是，我们介绍了一般形式的几何均值定义，然后我们定义了振生矩阵的任意操作员均值和功能计算。 这种新讨论的应用涉及从积极矩阵到增生矩阵的概括。这包括算术谐波均值比较，操作员的单调，安多的不平等，乔伊的不平等，安多·兹汉（Ando-Zhan）亚辅助不平等等等。
The main goal of this paper is to discuss the recent advancements of operator means for accretive matrices in a more general setting. In particular, we present the general form governing the well established definition of geometric mean, then we define arbitrary operator means and functional calculus for accretive matrices. Applications of this new discussion involve generalizations of known inequalities from the setting of positive matrices to that of accretive matrices. This includes the arithmetic-harmonic mean comparisons, monotony of operator means, Ando's inequality, Choi's inequality, Ando-Zhan subadditive inequality and much more.
