title: Some means inequalities for positive operators in Hilbert spaces.
abstract: 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.
authors.affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240 China.
authors.forename: Jin
authors.initials: J
authors.lastname: Liang
authors.affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240 China.
authors.forename: Guanghua
authors.initials: G
authors.lastname: Shi
keywords: Hilbert space; means inequalities; positive linear operators