On Variance and Covariance for Bounded Linear Operators

作     者：Chia Shiang LIN 

作者机构：Department of Mathematics Bishop's University Lennoxville P. Q. J1M 1Z7. Canada 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2001年第17卷第4期

页      面：657-668页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

主　　题：Covariance-variance inequality Bernstein inequality Reid’s inequality Furuta inequality Lowner-Heinz formula 

摘      要：In this paper we initiate a study of covariance and variance for two operators on a Hilbert space. proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy- Schwarz inequality. As for applications of the c-v inequality we provc uniformly the Bernstein-type inequalities and equalities. and show the generalized Heinz-Kato-Furuta-type inequalities and equalities. from which a generalization and sharpening of Reid’s inequlality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.