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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.13 No.2

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On Generalization of Covariance and Variance

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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.
Lin, C. (2006). On Generalization of Covariance and Variance. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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