Advertisement

Commutator Approximants

  • Philip J. Maher
Chapter

Abstract

We study approximation by commutators AXXA, by generalized commutators AXXB and by self–commutators XXXX for varying X in the context of \(\mathcal{L}(H)\) and \(\mathcal{C}_{p}\).

Bibliography

  1. 1.
    J.G. Aiken, J.A. Erdos, J.A. Goldstein, Unitary approximation of positive operators. Ill. J. Math. 24, 61–72 (1980)MathSciNetzbMATHGoogle Scholar
  2. 3.
    N.I. Akheiser, I.M. Glazman, in Theory of Linear Operators in Hilbert Space, vol. II (Unger, New York, 1963)Google Scholar
  3. 5.
    J. Anderson, On normal derivations. Proc. Am. Math. Soc. 38, 135–140 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 6.
    J. Anderson, C. Foias, Properties which normal operators share with derivations and related operators. Pac. J. Math. 61, 313–325 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 10.
    S. Bouali, S. Cherki, Approximation by generalized commutators. Acta Sci. Math. (Szeged) 63, 272–278 (1997)MathSciNetzbMATHGoogle Scholar
  6. 13.
    H. Dunford, J.T. Schwartz, Linear Operators, Part II (Interscience, New York, 1963)zbMATHGoogle Scholar
  7. 15.
    J.A. Erdos, On the trace of a trace class operator. Bull. Lond. Math. Soc. 6, 47–50 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 19.
    P.R. Halmos, Commutators of operators, II. Am. J. Math. 76, 191–198 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 23.
    P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)CrossRefzbMATHGoogle Scholar
  10. 26.
    D.C. Kleinecke, On operator commutators. Proc. Am. Math. Soc. 8, 535–536 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 32.
    P.J. Maher, Commutator approximants. Proc. Am. Math. Soc. 115, 995–1000 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 35.
    P.J. Maher, Self-commutator approximants. Proc. Am. Math. Soc. 134, 157–165 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 36.
    P.J. Maher, Commutator and self-commutator approximants, II. Filomat 24(4), 1–7 (2010). www.pmf.ni.ac,yu/sajt/publiRacije/publiKacije–pocetna Google Scholar
  14. 38.
    E.W. Packel, Functional Analysis: A Short Course (Intertext, New York, 1974)zbMATHGoogle Scholar
  15. 40.
    J.R. Ringrose, Compact Non-Self-Adjoint Operators (Van Nostrand Rheinhold, London, 1971)zbMATHGoogle Scholar
  16. 42.
    P.V. Shirokov, Proof of a conjecture of Kaplansky. Usp. Mat. Nauk 11, 161–168 (1956)MathSciNetGoogle Scholar
  17. 44.
    H. Wielandt, Ueber die Unbeschränktheit der Operatoren des Quantenmechanik. Math. Ann. 121, 21 (1949)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 45.
    A. Wintner, The unboundedness of quantum-mechanical matrices. Phys. Rev. 71, 738–739 (1947)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Philip J. Maher
    • 1
  1. 1.LondonUK

Personalised recommendations