关于算子和与绝对值的和的Lieb函数的不等式  

Lieb Function Inequalities for the Sum of Operators and the Sum of Absolute Values

作　　者：周吉 时硕 张云[1] ZHOU Ji;SHI Shuo;ZHANG Yun(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)

机构地区：[1]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《淮北师范大学学报（自然科学版）》2024年第1期16-20,共5页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽高校自然科学研究重大项目(KJ2021ZD0058);安徽省自然科学基金项目(1708085QA05);淮北师范大学研究生创新基金项目(CX2023046);淮北师范大学经费拓展研究项目(2023ZK035)。

摘　　要：为研究算子和与绝对值的和的Lieb函数不等式,文章借助Lieb函数的一种等价刻画,利用分块算子矩阵的技巧,得到一系列关于算子和与Hadamard积的Lieb函数的不等式,推广Lieb和Horn等的结果。同时,在此基础上改进关于Abu-Omar和Kittaneh算子矩阵的数值半径不等式,进而丰富矩阵不等式的相关理论。In order to study the Lieb function inequalities of the sum of operators and the sum of absolute values,Lieb function inequalities related to the sum of operators and the sum of their absolute values are obtained by using the equivalent of Lieb function and the technique of block operator matrix.These inequalities generalize the previous results of Lieb,Horn et al.Furthermore,there is an improvement of numerical radius inequality about Abu-Omar and Kittaneh for operator matrix given in this paper,which enriches the theory of matrix inequalities.

关 键 词：Lieb函数 HADAMARD积 数值半径 算子矩阵 

分 类 号：O177.1[理学—数学]