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On some inequalities for numerical radius of operators in Hilbert spaces

Silvestru Sever Dragomir
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2017.06|한국수학논문집 (Korean Journal of Mathematics)|제25권 제2호|pp. 247-259

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참고문헌

키워드

Schwarz inequalityBuzano inequalityNumerical radiusOperator normOperator inequalities
주제분류수학

초록

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.

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.

참고문헌 (28)

  1. M. L. Buzano, "Generalizzazione della diseguaglianza di Cauchy-Schwarz (Ital-ian)", Rend. Sem. Mat. Univ. e Politech. Torino, 31, pp.405~409 (1971)
  2. S. S. Dragomir, "Some refinements of Schwartz inequality", Simpozionul de Matematici si Aplicatii, Timisoara, pp.13~16 (1985)
  3. S. S. Dragomir, "Gruss inequality in inner product spaces", The Australian Math Soc. Gazette, 26(2), pp.66~70 (1999)
  4. S. S. Dragomir, "A generalization of Gruss' inequality in inner product spaces and applications", J. Math. Anal. Appl, 237, pp.74~82 (1999)
  5. S. S. Dragomir, "Some Gruss type inequalities in inner product spaces", J. Inequal. Pure & Appl. Math, 4(2) (2003)
  6. S. S. Dragomir, "Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces", J. Inequal. Pure & Appl. Math, 5(3) (2004)
  7. S. S. Dragomir, "New reverses of Schwarz, triangle and Bessel inequalities in inner product spaces", Austral. J. Math. Anal. & Applics, 1(1) (2004)
  8. S. S. Dragomir, "On Bessel and Gruss inequalities for orthornormal families in inner product spaces", Bull. Austral. Math. Soc, 69(2), pp.327~340 (2004)
  9. S. S. Dragomir, "Advances in Inequalities of the Schwarz, Gruss and Bessel Type in Inner Product Spaces" (2005), Nova Science Publishers Inc
  10. S. S. Dragomir, "Reverses of the Schwarz inequality in inner product spaces generalising a Klamkin-McLenaghan result", Bull. Austral. Math. Soc, 73(1), pp.69~78 (2006)
  11. S. S. Dragomir, "Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces" (2007), Nova Science Publishers, Inc.
  12. S. S. Dragomir, "Inequalities for the norm and the numerical radius of linear operators in Hilbert spaces", Demonstratio Math, 40(2), pp.411~417 (2007)
  13. S. S. Dragomir, "Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces", Tamkang J. Math, 39(1), pp.1~7 (2008)
  14. S. S. Dragomir, "Some new Gruss' type inequalities for functions of selfadjoint operators in Hilbert spaces", RGMIA Res. Rep. Coll, 11(e) (2008)
  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)
  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)
  17. S. S. Dragomir, "Inequalities for the Cebysev functional of two functions of selfadjoint operators in Hilbert spaces", Aust. J. Math. Anal. & Appl, 6, pp.1~58 (2009)
  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(9-10), pp.757~767 (2009)
  19. S. S. Dragomir, "Operator Inequalities of the Jensen, Cebysev and Gruss Type", pp.xii+121~ (2012), Springer
  20. S. S. Dragomir, "Operator Inequalities of Ostrowski and Trapezoidal Type", pp.x+112~ (2012), Springer
  21. S. S. Dragomir, "Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces", pp.x+120~ (2013), Springer
  22. S. S. Dragomir, "Norm inequalities of Cebysev type for power series in Banach algebras", Preprint RGMIA Res. Rep. Coll, 16 (2013)
  23. S. S. Dragomir, "On the superadditivity and monotonicity of Schwarz's inequality in inner product spaces", Contributions, Macedonian Acad. of Sci and Arts, 15(2), pp.5~22 (1994)
  24. S. S. Dragomir, "Some inequalities for Fourier coefficients in inner product spaces", Periodica Math. Hungarica, 32(3), pp.167~172 (1995)
  25. S. S. Dragomir, "The Chebyshev inequality in pre-Hilbertian spaces. II", Proceedings of the Third Symposium of Mathematics and its Applications, pp.75~78 (1989)
  26. S. S. Dragomir, "The Chebyshev inequality in pre-Hilbertian spaces. I", Proceedings of the Second Symposium of Mathematics and its Applications, pp.61~64 (1987)
  27. K. E. Gustafson, "Numerical Range" (1997), Springer-Verlag
  28. S. Kurepa, "Note on inequalities associated with Hermitian functionals", Glasnik Matematicki, 3(x23), pp.196~205 (1968)

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