# Some means inequalities for positive operators in Hilbert spaces

Journal of Inequalities and Applications, Jan 2017

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and show that the weighted multivariate operator geometric mean possess several attractive properties and means inequalities. MSC: 47A30, 47A63, 26D10, 26D20, 26E60.

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Jin Liang, Guanghua Shi. Some means inequalities for positive operators in Hilbert spaces, Journal of Inequalities and Applications, 2017, 14, DOI: 10.1186/s13660-016-1283-x