We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.
@article{bwmeta1.element.doi-10_2478_spma-2014-0015,
author = {Xuhua Liu and Tin-Yau Tam},
title = {Extensions of Three Matrix Inequalities to Semisimple Lie Groups},
journal = {Special Matrices},
volume = {2},
year = {2014},
zbl = {1308.15019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0015}
}
Xuhua Liu; Tin-Yau Tam. Extensions of Three Matrix Inequalities to Semisimple Lie Groups. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0015/
[1] Araki, H., On an inequality of Lieb and Thirring, Lett. Math. Phys. 19 (1990), 167–170. | Zbl 0705.47020
[2] Audenaert, K. M. R., On the Araki-Lieb-Thirring Inequality, Int. J. Inf. Syst. Sci. 4 (2008), 78–83. | Zbl 1156.15008
[3] Bhatia, R., “Matrix Analysis", Springer-Verlag, New Yor, 1997. | Zbl 0863.15001
[4] Helgason, S., “Differential Geometry, Lie Groups, and Symmetric Spaces”, Academic Press, 1978. | Zbl 0451.53038
[5] Hiai, F., Log-majorizations and norm inequalities for exponential operators, Linear Operators, Volume 38, p.119–181, Banach Center Publ., Polish Acad. Sci., Warsaw, 1997. | Zbl 0885.47003
[6] Horn, A., Doubly stochastic matrices and the diagonal of a rotation of matrix, Amer. J. Math. 76 (1954), 620–630. | Zbl 0055.24601
[7] Knapp, A. W., “Lie Groups beyond an Introduction", 2nd ed., Birkhäuser, 2002. | Zbl 1075.22501
[8] Kostant, B., On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455. | Zbl 0293.22019
[9] Lieb, E., and Thirring,W., in Studies inMathematical Physics (Eds. E. Lieb, B. Simon and A.Wightman), p.301–302, Princeton Press, 1976.
[10] Marshall, A. W., I. Olkin, and B. C. Arnold, “Inequalities: Theory of Majorization and its Applications (2nd ed.)”, Springer, 2011. | Zbl 1219.26003
[11] Simon, B., “Trace Ideals and Their Applications”, London Mathematical Society Lecture Note Series, 35, Cambridge Univ. Press, 1979. | Zbl 0423.47001
[12] Tam, T.Y., Kostant’s convexity theorem and the compact classical groups, Linear and Multilinear Algebra 43 (1997), 87–113. | Zbl 0894.22003
[13] Tam, T.Y., and Huang, H., An extension of Yamamoto’s theorem on the eigenvalues and singular values of a matrix, Journal of Math. Soc. Japan, 58 (2006), 1197–1202. | Zbl 1117.15008
[14] Tam, T.Y., Some exponential inequalities for semisimple Lie groups, A chapter of “Operators,Matrices and Analytic Functions”, 539–552, Oper. Theory Adv. Appl. 202, Birkhäuser Verlag, 2010. | Zbl 1192.15008
[15] Tam, T.Y., A. Horn’s result on matrices with prescribed singular values and eigenvalues, Electron. J. Linear Algebra 21 (2010), 25–27. | Zbl 1215.15022
[16] von Neumann, J., Some matrix-inequalities and metrization of matric-space, Tomsk. Univ. Rev., 1 (1937), 286–300.
[17] Zhan, X., “Matrix Inequality", Lecture Notes in Mathematics 1790, Springer, Berlin, 2002.