# Extensions of Three Matrix Inequalities to Semisimple Lie Groups

Special Matrices (2014)

- Volume: 2, Issue: 1, page 148-154, electronic only
- ISSN: 2300-7451

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topXuhua Liu, and Tin-Yau Tam. "Extensions of Three Matrix Inequalities to Semisimple Lie Groups." Special Matrices 2.1 (2014): 148-154, electronic only. <http://eudml.org/doc/267514>.

@article{XuhuaLiu2014,

abstract = {We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.},

author = {Xuhua Liu, Tin-Yau Tam},

journal = {Special Matrices},

keywords = {Araki-Lieb-Thirring inequality; positive definite matrices; semisimple Lie groups; log majorization; Kostant’s pre-order; Kostant's pre-order},

language = {eng},

number = {1},

pages = {148-154, electronic only},

title = {Extensions of Three Matrix Inequalities to Semisimple Lie Groups},

url = {http://eudml.org/doc/267514},

volume = {2},

year = {2014},

}

TY - JOUR

AU - Xuhua Liu

AU - Tin-Yau Tam

TI - Extensions of Three Matrix Inequalities to Semisimple Lie Groups

JO - Special Matrices

PY - 2014

VL - 2

IS - 1

SP - 148

EP - 154, electronic only

AB - We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.

LA - eng

KW - Araki-Lieb-Thirring inequality; positive definite matrices; semisimple Lie groups; log majorization; Kostant’s pre-order; Kostant's pre-order

UR - http://eudml.org/doc/267514

ER -

## References

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- [7] Knapp, A. W., “Lie Groups beyond an Introduction", 2nd ed., Birkhäuser, 2002. Zbl1075.22501
- [8] Kostant, B., On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455. Zbl0293.22019
- [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. Zbl1219.26003
- [11] Simon, B., “Trace Ideals and Their Applications”, London Mathematical Society Lecture Note Series, 35, Cambridge Univ. Press, 1979. Zbl0423.47001
- [12] Tam, T.Y., Kostant’s convexity theorem and the compact classical groups, Linear and Multilinear Algebra 43 (1997), 87–113. Zbl0894.22003
- [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. Zbl1117.15008
- [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. Zbl1192.15008
- [15] Tam, T.Y., A. Horn’s result on matrices with prescribed singular values and eigenvalues, Electron. J. Linear Algebra 21 (2010), 25–27. Zbl1215.15022
- [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.

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