International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Reverse of the Triangle Inequality in Hilbert C*-Modules

  • Nordine Bounader
  • Abdellatif Abdellatif Chahbi*
  • Samir Kabbaj

    * Corresponding author

    Abstract

    In this paper we prove the reverse of triangle inequality via Selberg's inequalities in the framework of Hilbert C*-modules.

    How to Cite

    N. Bounader, A. A. Chahbi, S. Kabbaj, Reverse of the Triangle Inequality in Hilbert C*-Modules, Int. J. Anal. Appl. 9 (2015), 29–38.

    BibTeX
    @article{Bounader2015,
      author  = {Bounader, Nordine and Chahbi, Abdellatif Abdellatif and Kabbaj, Samir},
      title   = {Reverse of the Triangle Inequality in Hilbert  C*-Modules},
      journal = {Int. J. Anal. Appl.},
      volume  = {9},
      year    = {2015},
      pages   = {29--38},
      doi     = {}
    }

    References

    • [1] A.H. Ansari and M.S.Moslehian, Refinement of reverse triangle inequality in inner product spaces.J. Inequalities in Pure and Applied Math., 6(2005). Article ID 64.
    • [2] A.H. Ansari and M.S.Moslehian, More on reverse triangle inequality in inner product spaces. Inter J. Math. Math Sci, 18(2005), 2883-2893.
    • [3] N.Bounader and A.Chahbi, Selberg type inequalities in Hilbert C*-modules. Int. Journal of Math. Analysis, 7 (2013), 385-391
    • [4] J.B. Diaz and F.T. Metcalf,A complementary triangle inequality in Hilbert and Banach spaces. Proc. Amer. Math. Soc., 17(1966), 88-97.
    • [5] S. Dragomir, Reverse of the triangle inequality via Selberg's and Boas-Bellman's inequalities.Facta universitatis (NIS), Ser. Math. Inform. 21(2006), 29C39
    • [6] S. S. Dragomir, M. Khosravi and M. S. Moslehian, Bessel type inequality in Hilbert C*- modules. Linear and Multilinear Algebra, 8(2010), 967-975.
    • [7] A. M. Fink, D.S. Mitrinovic and J. E.Pecaric Classical and new inequalities in analysis. Kluwer Academic, Dordrecht, 1993.
    • [8] M. Fujii, Selberg inequalty.(1991), 70-76.
    • [9] M. Fujii and R. Nakamoto, Simultaneous extensions of Selberg inequality and Heinz-KatoFuruta inequality. Nihonkai Math. J. 9(1998), 219-225.
    • [10] I. Kaplansky, Modules over operateur algebras. Amer. J. Math, (1953), 839-858.
    • [11] M.Kato, K.S. Saito and T. Tamura, Sharp triangle inequality and its reverse in Banach spaces. Math. Inegal. Appl. 10(2007), 451-460.
    • [12] M.Khosravi, H.Mahyar, M.S. Moslehyan,Reverse triangle inequality Hilbert C*-modules. J. Inequal. Pure Appl. Math, 10(2009), Article 110, 11 pages.
    • [13] E. C. Lance, Hilbert C*-modules. London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 210(1995).
    • [14] C.-S. Lin, Heinz's inequality and Bernstein's inequality. Proceedings of the American Mathematical society, 125(1997), 2319-2325.
    • [15] J.G. Murphy, C*-Algebras and operator theory. Academic Press, Boston, 1990.
    • [16] M. Nakai and T. Tada, The reverse triangle inequality in normed spaces. New Zealand J.math., 25(1996), 181-193.