On Generalization of Covariance and Variance

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2006, v.13 no.2, pp.137-149

Lin C.S. (DEPARTMENT OF MATHEMATICS, BISHOP'S UNIVERSITY)

Lin C.S.. (2006). ON GENERALIZATION OF COVARIANCE AND VARIANCE. 한국수학교육학회지시리즈B:순수및응용수학, 13(2), 137-149.

복사

Abstract

We introduce the notion of the generalized covariance and variance for bounded linear operators on Hilbert space, and prove that the generalized covariance-variance inequality holds. It turns out that the inequality is a useful formula in tile study of inequality involving linear operators in Hilbert spaces.

keywords: Cauchy-Schwarz inequality, convariance-variance inequality, extended convariance-variance inequality, Ostrowski inequality, Bernstein inequality, Reid's inequality, Furuta inequality, Heinz inequality, Heinz-Kato-Furuta inequality, Lowner-Heinz inequality

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논문 상세

Vol.13 No.2

ON GENERALIZATION OF COVARIANCE AND VARIANCE

On Generalization of Covariance and Variance

Abstract

한국수학교육학회지시리즈B:순수및응용수학