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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.13 No.2

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ON GENERALIZATION OF COVARIANCE AND VARIANCE

On Generalization of Covariance and Variance

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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. , 13(2), 137-149.

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

한국수학교육학회지시리즈B:순수및응용수학

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