Notes on matrix arithmetic-geometric mean inequalities

Linear Algebra and Its Applications

Volumn 308, Issue 1-3, 2000, Pages 203-211

  Bhatia, Rajendra ^a   Kittaneh, Fuad ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b UNIVERSITY OF JORDAN   (Jordan)

Author keywords

15A42; 15A60; 47A30; 47B05; 47B10; Arithmetic geometric mean; Majorisation; Singular values; Unitarily invariant norms

Indexed keywords

EID: 0034420259     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00048-3     Document Type: Article

References (9)

1. Ando T. Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl. 26:1979;203-241.
2. Bhatia R. Matrix Analysis. 1997;Springer, New York.
3. Bhatia R., Davis C. More matrix forms of the arithmetic-geometric mean inequality. SIAM J. Matrix Anal. 14:1993;132-136.
4. Bhatia R., Kittaneh F. On the singular values of a product of operators. SIAM J. Matrix Anal. 11:1990;272-277.
5. Kittaneh F. A note on the arithmetic-geometric mean inequality for matrices. Linear Algebra Appl. 171:1992;1-8.
6. Kosaki H. Arithmetic-geometric mean and related inequalities for operators. J. Funct. Anal. 156:1998;429-451.
7. E.H. Lieb, W.E. Thirring, Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, in: E. Lieb, B. Simon, A. Wightman (Eds.), Studies in Mathematical Physics, Princeton University Press, Princeton, NJ, 1976, pp. 269-303.
8. R.C. Thompson, Matrix Spectral Inequalitites, Conference Lecture Notes, Mathematical Sciences Lecture Series, Johns Hopkins University, Baltimore, MD, June 1988.
9. Zhan X. Inequalities for unitarily invariant norms. SIAM J. Matrix Anal. 20:1999;466-470.