Geometric Means and Tracy-Singh Products for Positive Operators - Ploymukda, Arnon; Chansangiam, Pattrawut (Communications in Mathematics and Applications, 2018)
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.