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2013 | 11 | 9 | 1698-1710
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Improved Heinz inequalities via the Jensen functional

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By virtue of convexity of Heinz means, in this paper we derive several refinements of Heinz norm inequalities with the help of the Jensen functional and its properties. In addition, we discuss another approach to Heinz operator means which is more convenient for obtaining the corresponding operator inequalities for positive invertible operators.
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Bibliografia
  • [1] Bhatia R., Matrix Analysis, Grad. Texts in Math., 169, Springer, New York, 1997
  • [2] Bhatia R., Positive Definite Matrices, Princeton Ser. Appl. Math., Princeton University Press, Princeton, 2007
  • [3] Bhatia R., Davis C., More matrix forms of the arithmetic-geometric mean inequality, SIAM J. Matrix Anal. Appl., 1993, 14(1), 132–136 http://dx.doi.org/10.1137/0614012
  • [4] Dragomir S.S., Pečarić J., Persson L.E., Properties of some functionals related to Jensen’s inequality, Acta Math. Hungar., 1996, 70(1–2), 129–143 http://dx.doi.org/10.1007/BF00113918
  • [5] Furuta T., Mićić Hot J., Pečarić J., Seo Y., Mond-Pečaric Method in Operator Inequalities, Monographs in Inequalities, 1, Element, Zagreb, 2005
  • [6] Hiai F., Kosaki H., Means for matrices and comparison of their norms, Indiana Univ. Math. J., 1999, 48(3), 899–936 http://dx.doi.org/10.1512/iumj.1999.48.1665
  • [7] Kittaneh F., On the convexity of the Heinz means, Integral Equations Operator Theory, 2010, 68(4), 519–527 http://dx.doi.org/10.1007/s00020-010-1807-6
  • [8] Kittaneh F., Krnić M., Lovričević N., Pečarić J., Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators, Publ. Math. Debrecen, 2012, 80(3–4), 465–478 http://dx.doi.org/10.5486/PMD.2012.5193
  • [9] Kittaneh F., Manasrah Y., Improved Young and Heinz inequalities for matrices, J. Math. Anal. Appl., 2010, 361(1), 262–269 http://dx.doi.org/10.1016/j.jmaa.2009.08.059
  • [10] Kittaneh F., Manasrah Y., Reverse Young and Heinz inequalities for matrices, Linear Multilinear Algebra, 2011, 59(9), 1031–1037 http://dx.doi.org/10.1080/03081087.2010.551661
  • [11] Klaričić Bakula M., Matić M., Pečarić J., On inequalities complementary to Jensen’s inequality, Mat. Bilten, 2008, 32, 17–27
  • [12] Krnić M., Lovričević N., Pečarić J., Jensen’s operator and applications to mean inequalities for operators in Hilbert space, Bull. Malays. Math. Sci. Soc., 2012, 35(1), 1–14
  • [13] Kubo F., Ando T., Means of positive linear operators, Math. Ann., 1979/80, 246(3), 205–224 http://dx.doi.org/10.1007/BF01371042
  • [14] Mitrinović D.S., Pečarić J.E., Fink A.M., Math. Appl. (East European Ser.), 61, Classical and New Inequalities in Analysis, Kluwer, Dordrecht, 1993
  • [15] Simon B., Trace Ideals and Their Applications, London Math. Soc. Lecture Note Ser., 35, Cambridge University Press, Cambridge-New York, 1979
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bwmeta1.element.doi-10_2478_s11533-013-0270-4
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