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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 5

Issues

Some reverse and numerical radius inequalities

Mohsen Shah Hosseini / Mohsen Erfanian Omidvar
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0174

Abstract

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

ω(TU±U*T)2ω(T2)+T±T*2.

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

MSC 2010: Primary 47A12; 47A62; Secondary 47B15; 47B47; 46C15

Keywords: numerical radius; operator norm; norm inequality

References

  • [1]

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

  • [2]

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

  • [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.Google Scholar

  • [4]

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

  • [5]

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

  • [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.Google Scholar

  • [7]

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

  • [8]

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

  • [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.Google Scholar

About the article

Received: 2017-03-30

Accepted: 2017-07-07

Published Online: 2018-10-20

Published in Print: 2018-10-25


Communicated by Werner Timmermann


Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1121–1128, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0174.

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