On Variance and Covariance for Bounded Linear Operators |
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Authors: | Chia Shiang Lin |
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Institution: | (1) Department of Mathematics, Bishop's University, Lennoxville, P. Q. J1M 1Z7, Canada, E-mail: plin@ubishops.ca, CA |
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Abstract: | 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 prove
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 inequality 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.
Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000 |
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Keywords: | Covariance-variance inequality Bernstein inequality Reid's inequality Furuta inequality L?wner-Heinz formula |
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