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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access December 11, 2014

Numerical Radius Inequalities for Finite Sums of Operators

  • Alireza Kamel Mirmostafaee EMAIL logo , Omid Pourbahari Rahpeyma and Mohsen Erfanian Omidvar
From the journal Demonstratio Mathematica

Abstract

In this paper, we obtain some sharp inequalities for numerical radius of finite sums of operators. Moreover, we give some applications of our result in estimation of spectral radius. We also compare our results with some known results.

References

[1] R. Bhatia, Matrix Analysis, Grad. Texts in Math. 169, Springer, New York, 1997.10.1007/978-1-4612-0653-8Search in Google Scholar

[2] H. Bohr, A theorem concerning power series, Proc. Lond. Math. Soc. 2(13) (1914), 1-5.10.1112/plms/s2-13.1.1Search in Google Scholar

[3] S. S. Dragomir, Power inequalities for the numerical radius of a product of two operators in Hilbert spaces, Sarajevo J. Math. 5(18) (2009), 269-278.Search in Google Scholar

[4] M. Fujii, R. Nakamoto, H. Watanabe, The Heinz-Kato-Furuta inequality and hyponormal operators, Math. Japon. 40 (1994), 469-472.Search in Google Scholar

[5] K. E. Gustafsun, D. K. M. Rao, Numerical Range, Springer-Verlag, New York, 1997.10.1007/978-1-4613-8498-4_1Search in Google Scholar

[6] M. EL. Haddad, F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 182(2) (2007), 133-140.10.4064/sm182-2-3Search in Google Scholar

[7] P. R. Halmos, A Hilbert Space Problem Book, 2nd ed. Grad. Texts in Math. 19, Springer, New York, 1982.10.1007/978-1-4684-9330-6Search in Google Scholar

[8] G. H. Hardy, J. E. Littewood, G. Polya, Inequalities, 2nd ed, Cambridge University Press, Cambridge, 1988.Search in Google Scholar

[9] F. Kittaneh, Nots on some inequalities for Hilbert space operators, Publ. Res. Inst. Math. Sci. 24(2) (1988), 283-293.10.2977/prims/1195175202Search in Google Scholar

[10] F. Kittaneh, Numerical radius inequalities for Hilbert space operators, Studia Math. 168(1) (2005), 73-80.10.4064/sm168-1-5Search in Google Scholar

[11] F. Kittaneh, Spectral radius inequalities for Hilbert space operator, Proc. Amer. Math. Soc. 134(2) (2005), 385-390.10.1090/S0002-9939-05-07796-8Search in Google Scholar

[12] F. Kittaneh, Commutator inequalities associated with the polar decomposition, Proc. Amer. Math. Soc. 120(5) (2002), 1279-1283.10.1090/S0002-9939-01-06197-4Search in Google Scholar

[13] K. Shebrawi, H. Albudawi, Numerical radius and operator norm inequalities, J. Inequal. Appl. 11 (2009).10.1155/2009/492154Search in Google Scholar

[14] J. S. Matharu, M. S. Moslehian, J. S. Aujla, Eigenvalue extensions of Bohr’s inequality, Linear Algebra Appl. 435(2) (2011), 270-276.10.1016/j.laa.2011.01.023Search in Google Scholar

[15] C. A. McCarthy, Cp , Israel J. Math. 5 (1967), 249-271.10.1007/BF02771613Search in Google Scholar

[16] M. E. Omidvar, M. S. Moslehian, A. Niknam, Some numerical radius inequalities for Hilbert space operator, Involve J. Math. 2(4) (2009), 469-476. 10.2140/involve.2009.2.471Search in Google Scholar

Received: 2013-3-25
Revised: 2013-5-13
Published Online: 2014-12-11
Published in Print: 2014-12-1

© by Alireza Kamel Mirmostafaee

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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