The Schwarz inequality via operator-valued inner product and the geometric operator mean

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  • 作用素値内積と作用素幾何平均を用いたシュワルツの不等式について

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In this papet, by virtue of the Cauchy-Schwarz operator inequality due to J.I. Fujii., we show the covariance-variance operator inequality via the geometric operator mean which differs from Bhatia-Davis's one and estimate the upper bounds. By our formulation:we bhow a Robertson type inequality associated to the conditionaı expectation on a finite von Nuemann algebra.

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