Some reverse and numerical radius inequalities

Mohsen Shah Hosseini 1  and Mohsen Erfanian Omidvar 1
  • 1 Department of Mathematics Mashhad Branch, Mashhad, Iran
Mohsen Shah Hosseini and Mohsen Erfanian Omidvar


In this paper, we present several numerical radius inequalities for Hilbert space operators. More precisely, we prove if T,UBH such that U is unitary, then


Also, we have compared our results with some known outcomes.

  • [1]

    BUZANO, M. L.: Generalizzazione della disiguaglianza di Cauchy-Schwaz (italian), Rend. Semin. Mat. Univ. Politec. Torino 31 (1971/73) (1974), 405–409.

  • [2]

    DRAGOMIR, S. S.: Reverse inequalities for the numerical radius of linear operators in Hilbert spaces, Bull. Aust. Math. Soc. 73(2) (2006), 255–262

  • [3]

    DRAGOMIR, S. S.: Some inequalities for the norm and the numerical radius of linear operators in Hilbert Spaces, Tamkang J. Math. 39(1) (2008), 1–7.

  • [4]

    DRAGOMIR, S. S.: Some refinements of Schwarz inequality, Suppozionul de Matematicasi Aplicatii, Polytechnical Institute Timisoara, Romania, 1-2 (1985), 13–16.

  • [5]

    GUSTAFSON, K. E.—RAO, D. K. M.: Numerical Range, Springer-Verlag, New York, Inc., 1997.

  • [6]

    HIRZALLAH, O.—KITTANEH, F.—SHEBRAWI, K.: Numerical radius inequalities for certain 2 x 2 operator matrices. Integr. Equ. Oper. Theory 71 (2011), 129–147.

  • [7]

    KITTANEH, F.: Norm inequalities for commutators of positive operators and applications, Math. Z. 258(4) (2008), 845–849.

  • [8]

    KITTANEH, F.: Numerical radius inequalities for Hilbert space operators, Studia Math. 168 (2005), 73–80.

  • [9]

    HOSSEINI, M. S.—OMIDVAR, M. E.: Some inequalities for the numerical radius for Hilbert space operators, Bull. Aust. Math. Soc. 94(3) (2016), 489–496.

Purchase article
Get instant unlimited access to the article.
Log in
Already have access? Please log in.

Journal + Issues

Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process.