Improved Heinz inequalities via the Jensen functional

Mario Krnić; Josip Pečarić

Open Mathematics (2013)

  • Volume: 11, Issue: 9, page 1698-1710
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Mario Krnić, and Josip Pečarić. "Improved Heinz inequalities via the Jensen functional." Open Mathematics 11.9 (2013): 1698-1710. <http://eudml.org/doc/269202>.

@article{MarioKrnić2013,
abstract = {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.},
author = {Mario Krnić, Josip Pečarić},
journal = {Open Mathematics},
keywords = {Heinz mean; Heinz norm inequalities; Heinz operator inequalities; Jensen functional; Monotonicity; Convex function; Unitarily invariant norm; Refinement; monotonicity; convex function; unitarily invariant norm; refinement},
language = {eng},
number = {9},
pages = {1698-1710},
title = {Improved Heinz inequalities via the Jensen functional},
url = {http://eudml.org/doc/269202},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Mario Krnić
AU - Josip Pečarić
TI - Improved Heinz inequalities via the Jensen functional
JO - Open Mathematics
PY - 2013
VL - 11
IS - 9
SP - 1698
EP - 1710
AB - 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.
LA - eng
KW - Heinz mean; Heinz norm inequalities; Heinz operator inequalities; Jensen functional; Monotonicity; Convex function; Unitarily invariant norm; Refinement; monotonicity; convex function; unitarily invariant norm; refinement
UR - http://eudml.org/doc/269202
ER -

References

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  9. [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 Zbl1180.15021
  10. [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 Zbl1225.15022
  11. [11] Klaričić Bakula M., Matić M., Pečarić J., On inequalities complementary to Jensen’s inequality, Mat. Bilten, 2008, 32, 17–27 Zbl1265.26073
  12. [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 Zbl1248.47018
  13. [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 Zbl0412.47013
  14. [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 Zbl0771.26009
  15. [15] Simon B., Trace Ideals and Their Applications, London Math. Soc. Lecture Note Ser., 35, Cambridge University Press, Cambridge-New York, 1979 Zbl0423.47001

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