Some means inequalities for positive operators in Hilbert spaces

被引：0
作者：
Jin Liang
Guanghua Shi
机构：
[1] Shanghai Jiao Tong University,School of Mathematical Sciences
来源：
Journal of Inequalities and Applications | / 2017卷
关键词：
means inequalities; positive linear operators; Hilbert space; 47A30; 47A63; 26D10; 26D20; 26E60;
D O I：
暂无
中图分类号：
学科分类号：
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.
引用
收藏
相关论文
共 21 条
[1]  
Abbas H(2014)A family of refinements of Heinz inequalities of matrices J. Inequal. Appl. 2014 102-117
[2]  
Mourad B(2016)Recent developments of matrix versions of the arithmetic-geometric mean inequality Ann. Funct. Anal. 7 1698-1710
[3]  
Fujii JI(2016)Reverses of Young and Heinz inequalities for positive linear operators J. Inequal. Appl. 2016 205-224
[4]  
Fujii M(2016)Tracial and majorisation Heinz mean-type inequalities for matrices J. Inequal. Appl. 2016 123-138
[5]  
Seo Y(2013)Improved Heinz inequalities via the Jensen functional Open Math. 11 1337-1344
[6]  
Zuo HL(1980)Means of positive linear operators Math. Ann. 246 51-60
[7]  
Malekinejad S(2014)Regular operator mappings and multivariate geometric means Linear Algebra Appl. 461 777-781
[8]  
Talebi S(2015)Refinements of the Heinz operator inequalities Linear Multilinear Algebra 63 undefined-undefined
[9]  
Ghazanfari AG(2015)Improved reverse arithmetic-geometric means inequalities for positive operators on Hilbert space Math. Inequal. Appl. 18 undefined-undefined
[10]  
Manjegani SM(2014)Some inequalities of operator monotone functions J. Math. Inequal. 8 undefined-undefined
123