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Two-Sided Bounds for the Weighted Operator Geometric Mean

Bounds sandwiching the weighted geometric mean of two invertible positive operators between a shifted unweighted geometric mean and the average of the weighted arithmetic and harmonic means, under a hypothesis pairing the weight with the operator order, proved by Kubo-Ando transfer to scalar calculus.

K-2SO Text

Operator inequalities among arithmetic mean, geometric mean and harmonic mean

Shigeru Furuichi (Nihon University; Journal of Mathematical Inequalities 8(3), 2014, 669-672; four pages) proves two-sided bounds relating the three classical means in their operator forms. The setti…