Some means inequalities for positive operators in Hilbert spaces

Journal of inequalities and applications

Jin Liang¹ 

关键词: means inequalities;    positive linear operators;    Hilbert space;    47A30;    47A63;    26D10;    26D20;    26E60;   

DOI  :  10.1186/s13660-016-1283-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY