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ON SOME INEQUALITIES FOR NUMERICAL RADIUS OF OPERATORS IN HILBERT SPACES

  • Dragomir, Silvestru Sever (Mathematics, College of Engineering & Science Victoria University)
  • Received : 2017.04.19
  • Accepted : 2017.06.02
  • Published : 2017.06.30

Abstract

By the use of inequalities for nonnegative Hermitian forms some new inequalities for numerical radius of bounded linear operators in complex Hilbert spaces are established.

Keywords

Schwarz inequality;Buzano inequality;Numerical radius;Operator norm;Operator inequalities

References

  1. M. L. Buzano, Generalizzazione della diseguaglianza di Cauchy-Schwarz (Ital-ian), Rend. Sem. Mat. Univ. e Politech. Torino 31 (1971/73), 405-409 (1974).
  2. S. S. Dragomir, Some refinements of Schwartz inequality, Simpozionul de Matematici si Aplicatii, Timisoara, Romania, 1-2 Noiembrie 1985, 13-16.
  3. S. S. Dragomir, Gruss inequality in inner product spaces, The Australian Math Soc. Gazette 26 (1999), No. 2, 66-70.
  4. S. S. Dragomir, A generalization of Gruss' inequality in inner product spaces and applications, J. Math. Anal. Appl. 237 (1999), 74-82. https://doi.org/10.1006/jmaa.1999.6452
  5. S. S. Dragomir, Some Gruss type inequalities in inner product spaces, J. Inequal. Pure & Appl. Math. 4 (2) (2003), Article 42. (Online http://jipam.vu.edu.au/article.php?sid=280).
  6. S. S. Dragomir, Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, J. Inequal. Pure & Appl. Math. 5(3) (2004), Article 76. (Online : http://jipam.vu.edu.au/article.php?sid=432).
  7. S. S. Dragomir, New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, Austral. J. Math. Anal. & Applics. 1(1) (2004), Article 1. (Online: http://ajmaa.org/cgi-bin/paper.pl?string=nrstbiips.tex).
  8. S. S. Dragomir, On Bessel and Gruss inequalities for orthornormal families in inner product spaces, Bull. Austral. Math. Soc. 69(2) (2004), 327-340. https://doi.org/10.1017/S0004972700036066
  9. S. S. Dragomir, Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces, Nova Science Publishers Inc, New York, 2005, x+249 p.
  10. S. S. Dragomir, Reverses of the Schwarz inequality in inner product spaces generalising a Klamkin-McLenaghan result, Bull. Austral. Math. Soc. 73 (1) (2006), 69-78. https://doi.org/10.1017/S0004972700038636
  11. S. S. Dragomir, Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces. Nova Science Publishers, Inc., New York, 2007. xii+243 pp. ISBN: 978-1-59454-903-8; 1-59454-903-6 (Preprint http://rgmia.org/monographs/advancees2.htm)
  12. S. S. Dragomir, Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces. Demonstratio Math. 40 (2007), no. 2, 411-417.
  13. S. S. Dragomir, Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces, Tamkang J. Math. 39 (2008), no. 1, 1-7.
  14. S. S. Dragomir, Some new Gruss' type inequalities for functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll. 11(e) (2008), Art. 12.
  15. S. S. Dragomir, Inequalities for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll. 11(e) (2008), Art. 17.
  16. S. S. Dragomir, Some inequalities for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces, RGMIA Res. Rep. Coll. 11(e) (2008), Art. 8.
  17. S. S. Dragomir, Inequalities for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces, Aust. J. Math. Anal. & Appl. 6 (2009), Issue 1, Article 7, pp. 1-58.
  18. S. S. Dragomir, Some inequalities for power series of selfadjoint operators in Hilbert spaces via reverses of the Schwarz inequality, Integral Transforms Spec. Funct. 20 (2009), no. 9-10, 757-767. https://doi.org/10.1080/10652460902910054
  19. S. S. Dragomir, Operator Inequalities of the Jensen, Cebysev and Gruss Type. Springer Briefs in Mathematics. Springer, New York, 2012. xii+121 pp. ISBN: 978-1-4614-1520-6.
  20. S. S. Dragomir, Operator Inequalities of Ostrowski and Trapezoidal Type. Springer Briefs in Mathematics. Springer, New York, 2012. x+112 pp. ISBN: 978-1-4614-1778-1.
  21. S. S. Dragomir, Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces. Springer Briefs in Mathematics. Springer, 2013. x+120 pp. ISBN: 978-3-319-01447-0; 978-3-319-01448-7.
  22. S. S. Dragomir, M. V. Boldea and C. Buse, Norm inequalities of Cebysev type for power series in Banach algebras, Preprint RGMIA Res. Rep. Coll. 16 (2013), Art. 73.
  23. S. S. Dragomir and B. Mond, On the superadditivity and monotonicity of Schwarz's inequality in inner product spaces, Contributions, Macedonian Acad. of Sci and Arts 15 (2) (1994), 5-22.
  24. S. S. Dragomir and B. Mond, Some inequalities for Fourier coefficients in inner product spaces, Periodica Math. Hungarica 32 (3) (1995), 167-172.
  25. S. S. Dragomir, J. Pecaric and J. Sandor, The Chebyshev inequality in pre-Hilbertian spaces. II. Proceedings of the Third Symposium of Mathematics and its Applications (Timisoara, 1989), 75-78, Rom. Acad., Timisoara, 1990. MR1266442 (94m:46033)
  26. S. S. Dragomir and J. Sandor, The Chebyshev inequality in pre-Hilbertian spaces. I. Proceedings of the Second Symposium of Mathematics and its Applications (Timisoara, 1987), 61-64, Res. Centre, Acad. SR Romania, Timisoara, 1988. MR1006000 (90k:46048).
  27. K. E. Gustafson and D. K. M. Rao, Numerical Range, Springer-Verlag, New York, Inc., 1997.
  28. S. Kurepa, Note on inequalities associated with Hermitian functionals, Glasnik Matematcki 3 (x23) (1968), 196-205.