Norm and anti-norm inequalities for positive semi-definite matrices

International Journal of Mathematics

Volumn 22, Issue 8, 2011, Pages 1121-1138

  Bourin, Jean Christophe ^a   Hiai, Fumio ^b  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

concave function; convex function; majorization; Matrix; operator; subadditivity; superadditivity; symmetric anti norm; symmetric norm; trace

Indexed keywords

EID: 80052101887     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X1100715X     Document Type: Article

References (11)

1. J. S. Aujla and J.-C. Bourin, Eigenvalues inequalities for convex and log-convex functions, Linear Algebra Appl. 424 (2007) 25-35. (Pubitemid 46693900)
2. R. Bhatia, Matrix Analysis (Springer, New York, 1996).
3. J.-C. Bourin, Hermitian operators and convex functions, J. Inequal. Pure Appl. Math. 6 (2005) 139.
4. J.-C. Bourin and E.-Y. Lee, Unitary orbits of Hermitian operators with convex or concave functions, preprint.
5. J.-C. Bourin and E.-Y. Lee, Concave functions of positive operators, sums, and congruences, J. Operator Theory 63 (2010) 151-157.
6. L. G. Brown and H. Kosaki, Jensen's inequality in semi-finite von Neumann algebras, J. Operator Theory 23 (1990) 3-19.
7. F. Hiai, Matrix analysis: Matrix monotone functions, matrix means, and majorization (GSIS selected lectures), Interdiscip. Inform. Sci. 16 (2010) 139-248.
8. F. Kubo and T. Ando, Means of positive linear operators, Math. Ann. 246 (1980) 205-224.
9. E.-Y. Lee, Extension of Rotfel'd theorem, to appear in Linear Algebra Appl.
10. B. Simon, Trace Ideals and Their Applications, 2nd edn. (Amer. Math. Soc., Providence, RI, 2005).
11. X. Zhan, The sharp Rado theorem for majorizations, Amer. Math. Monthly 110 (2003) 152-153. (Pubitemid 36256560)