一类有关正线性映射的算子不等式  

Some Operator Inequalities with Unital Positive Linear Map

作　　者：李乐 左红亮[1] 刘桃桃 王娅茹 洪国庆 LI Le;ZUO Hongliang;LIU Taotao;WANG Yaru;HONG Guoqing(College of Mathematics and Information Science,Henan Normal University,Henan Xinxiang 453007,Chin)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南大学学报（自然科学版）》2018年第4期499-504,共6页Journal of Henan University:Natural Science

基　　金：河南省基础与前沿技术研究项目(142300410167)

摘　　要：算子不等式是算子代数中的重要研究对象,其理论在数学的许多领域都发挥着举足轻重的作用.对于算子代数而言,刻画它上面的线性映射是非常有意义的,特别是在有限维的情况下,正线性映射在量子信息论里有很重要的应用.此外基于单位正线性映射在线性映射理论中的特殊性质,探究该映射下的相关问题也变得很有必要.本文是在线性映射和算子不等式的理论基础上,结合单位正线性映射的相关性质,应用已有算子平均不等式,进而得到若干在单位正线性映射下带有Kantorovich常数的相应算子平均不等式.Operator inequality is an important research object in operator algebra, and its theory plays a pivotal role in many fields of mathematics. For operator algebra, it is very meaningful to characterize the linear mapping, especially in the finite dimension space, positive linear mapping is very important in quantum information theory. In addition, it is necessary to explore the related problems under the unital positive linear mapping due to its special properties. In this paper, on the basis of the theory of linear mapping and operator inequality, combining the related properties of unital positive linear mapping, and applying the existing operator mean inequalities, the corresponding operator inequalities with Kantorovich constant were obtained under the unit positive linear mapping.

关 键 词：算子不等式 平均不等式 正线性映射 Kantorovich常数 

分 类 号：O177.2[理学—数学]