Complex Analysis and Operator Theory

, Volume 12, Issue 1, pp 195–205 | Cite as

Refinements of Inequalities Related to Landau–Grüss Inequalities for Elementary Operators Acting on Ideals Associated to p-Modified Unitarily Invariant Norms

  • Danko R. Jocić
  • Đorđe Krtinić
  • Milan Lazarević
  • Petar Melentijević
  • Stefan Milošević
Article
First Online:
Received:
Accepted:

Abstract

In this paper we find the explicit form for the equalizing term in the inequality related to Landau–Grüss inequality for elementary operators, which enabled us to refine inequalities related to operator Landau–Grüss norm inequalities for p-modifications of initarily invariant norms. Specially, for Schatten p-norms with \(p\ge 2\) those inequalities have additionally simplified form, which enables, among others, to analyze equality cases in considered operator inequalities. A broader family of mixed norms inequalities related to the operator Landau–Grüss inequality is also presented.

Keywords

Unitarily invariant norm Symmetrically norming function 

Mathematics Subject Classification

Primary 47A30 47A60 Secondary 47A65 47B10 47B15 46B20 15A57 15A60 
This is a preview of subscription content, log in to check access.

References

  1. 1.
    Bhatia, R.: Matrix Analysis. Springer, New York (1997)CrossRefMATHGoogle Scholar
  2. 2.
    Gohberg, I.C., Krein, M.G.: Introduction to the Theory of Linear Nonselfadjoint Operators, Transl. Math. Monographs, vol. 18. American Mathematical Society, Providence (1969)Google Scholar
  3. 3.
    Gohberg, I.C., Goldberg, S., Kaashoek, M.A.: Classes of Linear Operators, Operator Theory, vol. 49. Birkhauser, Basel (1990)MATHGoogle Scholar
  4. 4.
    Hirzallah, O., Kittaneh, F.: Clarkson inequalities for \(n\)-tuples of operators. Integr. Equ. Oper. Theory 60(3), 369–379 (2008)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Jocić, D.R.: The Cauchy–Schwarz norm inequality for elementary operators in Schatten ideals. J. Lond. Math. Soc. (2) 60(3), 925–934 (1999)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Jocić, D.R.: Cauchy–Schwarz norm inequalities for weak*-integrals of operator valued functions. J. Funct. Anal. 218(2), 318–346 (2005)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Jocić, D.R.: Multipliers of elementary operators and comparison of row and column space Schatten \(p\) norms. Linear Algebra Appl. 431(11), 2062–2070 (2009)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Jocić, D.R., Krtinić, Đ., Moslehian, M.S.: Landau and Grüss type inequalities for inner product type integral transformers on norm ideals. Math. Inequal. Appl. 16(1), 109–125 (2013)Google Scholar
  9. 9.
    Jocić, D.R., Milošević, S.: Refinements of operator Cauchy–Schwarz and Minkowski inequalities for \(p\)-modified norms and related norm inequalities. Linear Algebra Appl. 488, 284–301 (2016)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Schatten, R.: Norm Ideals of Completely Continuous Operators. Springer, Berlin (1960)CrossRefMATHGoogle Scholar
  11. 11.
    Simon, B.: Trace Ideals and Their Applications. Cambridge University Press, Cambridge (1979)MATHGoogle Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Danko R. Jocić
    • 1
  • Đorđe Krtinić
    • 1
  • Milan Lazarević
    • 1
  • Petar Melentijević
    • 1
  • Stefan Milošević
    • 1
  1. 1.Department of MathematicsUniversity of BelgradeBelgradeSerbia

Personalised recommendations