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arXiv · 1410.4905

Operator inequalities among arithmetic mean, geometric mean and harmonic mean

Shigeru Furuichi
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Abstract

We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive operators.

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Shigeru Furuichi. 2014-10-18. Operator inequalities among arithmetic mean, geometric mean and harmonic mean. https://doi.org/10.7153/jmi-08-49

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