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On Variance and Covariance for Bounded Linear Operators
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作者 Chia Shiang LIN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2001年第4期657-668,共12页
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... 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. 展开更多
关键词 covariance-variance inequality Bernstein inequality Reid’s inequality Furuta inequality Lowner-Heinz formula
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