Geometric Means and Tracy-Singh Products for Positive Operators

Arnon Ploymukda, Pattrawut Chansangiam


We investigate relationship between metric/spectral/Sagae-Tanabe geometric means for several positive operators and Tracy-Singh products in terms of identities and inequalities. In particular, we obtain various generalizations of arithmetic-geometric-harmonic means inequality and its reverse. Moreover, we introduce the weighted Sagae-Tanabe spectral geometric mean for several positive operators and deduce its properties related to Tracy-Singh products.


Metric (spectral) geometric mean; Sagae-Tanabe metric (spectral) geometric mean; Tensor product; Tracy-Singh product; Khatri-Rao product

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