A weakened version of Davis-Choi-Jensen’s inequality for normalised positive linear maps

• Dragomir, S. S. ^[1]
  1. [1] Victoria University

     Victoria University

     Australia

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 36, Nº. 1, 2017, págs. 81-94
• Idioma: inglés
• DOI: 10.4067/S0716-09172017000100005
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• Resumen

  • In this paper we show that the celebrated Davis-Choi-Jensen’s inequality for normalised positive linear maps can be extended in a weakened form for convex functions. A reverse inequality and applications for important instances of convex (concave) functions are also given.

• Referencias bibliográficas
  • Citas [1] M. D. Choi, Positive linear maps on C*-algebras. Canad. J. Math. 24, pp. 520—529, (1972).
  • [2] S. S. Dragomir, Some reverses of the Jensen inequality for functions of selfadjoint operators in Hilbert spaces. J. Inequal. Appl., Art....
  • [3] S. S. Dragomir, Operator Inequalities of the Jensen, Čebyšev and Grüss Type. Springer Briefs in Mathematics. Springer, New York, xii+121...
  • [4] S. S. Dragomir and N. M. Ionescu, Some converse of Jensen’s inequality and applications. Rev. Anal. Numér. Théor. Approx. 23, No. 1, pp....
  • [5] C. A. McCarthy, cp, Israel J. Math., 5, pp. 249-271, (1967).
  • [6] B. Mond and J. Pečarić, Convex inequalities in Hilbert space, Houston J. Math., 19, pp. 405-420, (1993).
  • [7] J. Pečarić, T. Furuta, J. Mićić Hot and Y. Seo, Mond- Pečarić Method in Operator Inequalities. Inequalities for Bounded Selfadjoint Operators...