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arxiv: 1410.4905 · v1 · pith:AHWGEMQ6new · submitted 2014-10-18 · 🧮 math.FA

Operator inequalities among arithmetic mean, geometric mean and harmonic mean

classification 🧮 math.FA
keywords meanweightedgeometricarithmeticboundgiveharmonicinequalities
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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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