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Tytuł artykułu

Extensions of Three Matrix Inequalities to Semisimple Lie Groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give extensions of inequalities of Araki-Lieb-Thirring, Audenaert, and Simon, in the context of semisimple Lie groups.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Opis fizyczny
Daty
otrzymano
2014-07-04
zaakceptowano
2014-09-14
online
2014-11-07
Twórcy
autor
  • Department of Mathematics, The University of Tennessee at Chattanooga, Chattanooga,
    TN 37403, USA
autor
  • Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849, USA
Bibliografia
  • [1] Araki, H., On an inequality of Lieb and Thirring, Lett. Math. Phys. 19 (1990), 167–170.
  • [2] Audenaert, K. M. R., On the Araki-Lieb-Thirring Inequality, Int. J. Inf. Syst. Sci. 4 (2008), 78–83.
  • [3] Bhatia, R., “Matrix Analysis", Springer-Verlag, New Yor, 1997.
  • [4] Helgason, S., “Differential Geometry, Lie Groups, and Symmetric Spaces”, Academic Press, 1978.
  • [5] Hiai, F., Log-majorizations and norm inequalities for exponential operators, Linear Operators, Volume 38, p.119–181, BanachCenter Publ., Polish Acad. Sci., Warsaw, 1997.
  • [6] Horn, A., Doubly stochastic matrices and the diagonal of a rotation of matrix, Amer. J. Math. 76 (1954), 620–630.
  • [7] Knapp, A. W., “Lie Groups beyond an Introduction", 2nd ed., Birkhäuser, 2002.
  • [8] Kostant, B., On convexity, the Weyl group and the Iwasawa decomposition, Ann. Sci. École Norm. Sup. (4) 6 (1973), 413–455.
  • [9] Lieb, E., and Thirring,W., in Studies inMathematical Physics (Eds. E. Lieb, B. Simon and A.Wightman), p.301–302, PrincetonPress, 1976.
  • [10] Marshall, A. W., I. Olkin, and B. C. Arnold, “Inequalities: Theory of Majorization and its Applications (2nd ed.)”, Springer,2011.
  • [11] Simon, B., “Trace Ideals and Their Applications”, London Mathematical Society Lecture Note Series, 35, Cambridge Univ.Press, 1979.
  • [12] Tam, T.Y., Kostant’s convexity theorem and the compact classical groups, Linear and Multilinear Algebra 43 (1997), 87–113.
  • [13] Tam, T.Y., and Huang, H., An extension of Yamamoto’s theorem on the eigenvalues and singular values of a matrix, Journal ofMath. Soc. Japan, 58 (2006), 1197–1202.
  • [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.
  • [15] Tam, T.Y., A. Horn’s result on matrices with prescribed singular values and eigenvalues, Electron. J. Linear Algebra 21 (2010),25–27.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_spma-2014-0015
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