Skip to main content

Commutator Approximants

  • Chapter
  • First Online:
  • 492 Accesses

Abstract

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

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  1. J.G. Aiken, J.A. Erdos, J.A. Goldstein, Unitary approximation of positive operators. Ill. J. Math. 24, 61–72 (1980)

    MathSciNet  MATH  Google Scholar 

  2. N.I. Akheiser, I.M. Glazman, in Theory of Linear Operators in Hilbert Space, vol. II (Unger, New York, 1963)

    Google Scholar 

  3. J. Anderson, On normal derivations. Proc. Am. Math. Soc. 38, 135–140 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. J. Anderson, C. Foias, Properties which normal operators share with derivations and related operators. Pac. J. Math. 61, 313–325 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Bouali, S. Cherki, Approximation by generalized commutators. Acta Sci. Math. (Szeged) 63, 272–278 (1997)

    MathSciNet  MATH  Google Scholar 

  6. H. Dunford, J.T. Schwartz, Linear Operators, Part II (Interscience, New York, 1963)

    MATH  Google Scholar 

  7. J.A. Erdos, On the trace of a trace class operator. Bull. Lond. Math. Soc. 6, 47–50 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. P.R. Halmos, Commutators of operators, II. Am. J. Math. 76, 191–198 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  9. P.R. Halmos, A Hilbert Space Problem Book, 2nd edn. (Springer, New York, 1974)

    Book  MATH  Google Scholar 

  10. D.C. Kleinecke, On operator commutators. Proc. Am. Math. Soc. 8, 535–536 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  11. P.J. Maher, Commutator approximants. Proc. Am. Math. Soc. 115, 995–1000 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. P.J. Maher, Self-commutator approximants. Proc. Am. Math. Soc. 134, 157–165 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. 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. E.W. Packel, Functional Analysis: A Short Course (Intertext, New York, 1974)

    MATH  Google Scholar 

  15. J.R. Ringrose, Compact Non-Self-Adjoint Operators (Van Nostrand Rheinhold, London, 1971)

    MATH  Google Scholar 

  16. P.V. Shirokov, Proof of a conjecture of Kaplansky. Usp. Mat. Nauk 11, 161–168 (1956)

    MathSciNet  Google Scholar 

  17. H. Wielandt, Ueber die Unbeschränktheit der Operatoren des Quantenmechanik. Math. Ann. 121, 21 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  18. A. Wintner, The unboundedness of quantum-mechanical matrices. Phys. Rev. 71, 738–739 (1947)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Maher, P.J. (2017). Commutator Approximants. In: Operator Approximant Problems Arising from Quantum Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61170-9_4

Download citation

Publish with us

Policies and ethics