Extension of Wang-Gong monotonicity result in semisimple Lie groups

 Access to full text

 Full (PDF)

1. [1] H. Araki, On an inequality of Lieb and Thirring, Lett. Math. Phys. 19, (1990) 167–170. Zbl0705.47020
2. [2] K. M. R. Audenaert, On the Araki-Lieb-Thirring inequality, Int. J. Inform. Sys. Sci. 4, (2008) 78–83. Zbl1156.15008
3. [3] K. M. R. Audenaert, A Lieb-Thirring inequality for singular values, Linear Algebra Appl. 430, (2009) 3053–3057. Zbl1168.15014
4. [4] R. Bhatia, “Matrix Analysis", Springer-Verlag, New York, 1997. 
5. [5] P.J. Bushell, and G.B. Trustrum, Trace inequalities for positive definite matrix power products, Linear Algebra Appl. 132 (1990), 173–178. Zbl0701.15015
6. [6] K.J. Le Couteur, Representation of the function tr (exp(A − ʎB)) as a Laplace transform with positive weight and somematrix inequalities, J. Phys. A 13, (1980), 3147–3159. Zbl0446.44002
7. [7] S. Helgason, “Differential Geometry, Lie Groups, and Symmetric Spaces”, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Zbl0451.53038
8. [8] R. Horn, and C. Johnson, “Matrix analysis (2nd ed.)”, Cambridge University Press, Cambridge, 2013. Zbl1267.15001
9. [9] A. W. Knapp, “Lie Groups beyond an Introduction", 2nd ed., Birkhäuser Boston, Inc., Boston, MA, 2002. Zbl1075.22501
10. [10] B. Kostant, On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455. Zbl0293.22019
11. [11] E. Lieb, andW. Thirring, in “Studies inMathematical Physics" (Eds. E. Lieb, B. Simon and A.Wightman), p.301–302, Princeton Press, 1976. 
12. [12] X. Liu, M. Liao, and T.Y. Tam, Geometric mean for symmetric spaces of noncompact type, Journal of Lie Theory 24 (2014), 725–736. Zbl1331.15011
13. [13] X. Liu, and T.Y. Tam, Extensions of three matrix inequalities to semisimple Lie groups, Special Matrices, 2 (2014), 148–154. Zbl1308.15019
14. [14] M. Marcus, An eigenvalues inequality for the product of normal matrices, Amer. Math. Monthly, 63 (1956), 173–174. Zbl0070.01304
15. [15] A. W. Marshall, I. Olkin, and B. C. Arnold, “Inequalities: Theory of Majorization and its Applications (2nd ed.)”, Springer, New York, 2011. Zbl1219.26003
16. [16] T.Y. Tam, and H. Huang, An extension of Yamamoto’s theorem on the eigenvalues and singular values of a matrix, Journal of Math. Soc. Japan, 58 (2006), 1197–1202. Zbl1117.15008
17. [17] T.Y. Tam, Some exponential inequalities for semisimple Lie groups, A chapter of “Operators, Matrices and Analytic Functions”, 539–552, Oper. Theory Adv. Appl. 202, Birkhäuser Verlag, Basel, 2010. Zbl1192.15008
18. [18] B.Y. Wang, and M.P. Gong, Some eigenvalue inequalities for positive semidefinite matrix power products, Linear Algebra Appl. 184 (1993), 249–260. Zbl0773.15009
19. [19] B.Y. Wang, and F. Zhang, Trace and eigenvalue inequalities for ordinary and hadamard products of positive semidefinite hermitian matrices, SIAM J. Matrix Anal. Appl., 16 (1995), 1173–1183. Zbl0855.15009
20. [20] X. Zhan, “Matrix Inequalities”, Lecture Notes in Mathematics 1790, Springer-Verlag, Berlin, 2002. Zbl1018.15016