Norm inequalities related to the arithmetic–geometric mean inequalities for positive semidefinite matrices

被引：0
作者：
Mostafa Hayajneh
Saja Hayajneh
Fuad Kittaneh
机构：
[1] Yarmouk University,Department of Mathematics
[2] The University of Jordan,Department of Mathematics
来源：
Positivity | 2018年 / 22卷
关键词：
Unitarily invariant norm; Hilbert–Schmidt norm; Singular value; Trace; Positive semidefinite matrix; Inequality; Primary 15A60; Secondary 15A18; 15A42; 47A30; 47B15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we propose three new matrix versions of the arithmetic–geometric mean inequality for unitarily invariant norms, which stem from the fact that the Heinz mean of two positive real numbers interpolates between the geometric and arithmetic means of these numbers. Related trace inequalities are also presented.
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页码：1311 / 1324
页数：13
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  • [1] Ando T(1999)Norm inequalities related to operator monotone functions Math. Ann. 315 771-780
  • [2] Zhan X(2000)Trace inequalities for multiple products of two matrices Math. Inequal. Appl. 3 307-318
  • [3] Ando T(2015)A norm inequality for pairs of commuting positive semidefinite matrices Electron. J. Linear Algebra 30 80-84
  • [4] Hiai F(2014)Trace inequalities for products of positive definite matrices J. Math. Phys. 55 013509-136
  • [5] Okubo K(1993)More matrix forms of the arithmetic–geometric mean inequality SIAM J. Matrix Anal. 14 132-773
  • [6] Audenaert K(2015)Inequalities related to Bourin and Heinz means with a complex parameter J. Math. Anal. Appl. 426 765-907
  • [7] Bhatia R(2006)Matrix versions of some classical inequalities Linear Algebra Appl. 416 890-691
  • [8] Bhatia R(2009)Matrix subadditivity inequalities and block-matrices Int. J. Math. 20 679-389
  • [9] Davis C(2013)Lieb–Thirring trace inequalities and a question of Bourin J. Math. Phys. 54 033504-232
  • [10] Bottazzi T(2013)Trace inequalities and a question of Bourin Bull. Aust. Math. Soc. 88 384-86
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