Wielandt不等式和Kantorovich不等式的一些推广  

Some Extensions of Wielandt and Kantorovich Inequalities

作　　者：刘建忠[1] 

机构地区：[1]江苏技术师范学院基础部,常州213001

出　　处：《工程数学学报》2007年第5期943-946,共4页Chinese Journal of Engineering Mathematics

基　　金：江苏技术师范学院引进人员科研项目(Kyy05524).

摘　　要：本文证明内积空间中的两个不等式,并由这些不等式导出Hilbert空间中关于有界自伴算子、有界可逆算子及正定算子的若干不等式,所获结果推广了关于正定矩阵著名的Wielandt不等式和Kantorovich不等式。同时给出了Cauchy-Schwarz不等式的一些改进形式。最后,作为应用,研究了一些新的积分不等式。By proving two inequalities in the inner product space, some inequalities for bounded self-adjoint operator, bounded invertible operator and positive definite operator in Hilbert space are derived. These results extend the famous Wielandt inequality and the Kantorovich inequality for the positive definite matrix. Furthermore, some improvement forms of the Cauehy-Sehwarz inequality are given. As an application of the obtained results, some new integral inequalities are also studied.

关 键 词：KANTOROVICH不等式 WIELANDT不等式 HILBERT空间 线性算子 

分 类 号：O151.21[理学—数学] O177.1[理学—基础数学]