Skip to main content

Locality and differential operators on C*-algebras, II

  • Conference paper
  • First Online:
Operator Algebras and their Connections with Topology and Ergodic Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1132))

  • 1283 Accesses

Abstract

A characterization in terms of locality is given of certain differential operators on a C*-algebra. These differential operators are polynomials in the generator of a one-parameter group of automorphisms of the C*-algebra, with coefficients in the centre of the algebra. (More precisely, the coefficients may be central multipliers of a certain two-sided ideal of the algebra.)

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Albrecht and M. Neumann, "Local operators between spaces of ultradifferentiable functions and ultradistributions", Manuscripta Math. 38 (1982) 131–161.

    Article  MathSciNet  MATH  Google Scholar 

  2. C.J.K. Batty, "Derivations on compact spaces", Proc. London Math. Soc. (3) 42 (1981) 299–330.

    Article  MathSciNet  MATH  Google Scholar 

  3. C.J.K. Batty, "Local operators and derivations on C*-algebras", preliminary version (1983).

    Google Scholar 

  4. O. Bratteli, T. Digernes, and D.W. Robinson, "Relative locality of derivations", preprint (1983).

    Google Scholar 

  5. O. Bratteli, G.A. Elliott, and D.E. Evans, "Locality and differential operators on C*-algebras", preprint (1983).

    Google Scholar 

  6. O. Bratteli, F. Goodman, and P.E.T. Jørgensen, "Unbounded derivations tangential to compact groups of automorphisms II", preprint (1983).

    Google Scholar 

  7. O. Bratteli and P.E.T. Jørgensen, "Unbounded derivations tangential to compact groups of automorphisms", J. Functional Analysis 48 (1982) 107–133.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Bratteli and D.W. Robinson, "Operator algebras and quantum statistical mechanics, I and II", Springer-Verlag, Berlin-Heidelberg-New York, 1979 and 1981.

    Book  MATH  Google Scholar 

  9. C. Davis, "The Toeplitz-Hausdorff theorem explained", Canad. Math. Bull. 14 (1971) 245–246.

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Dixmier, "Dual et quasi-dual d’une algèbre de Banach involutive" Trans. Amer. Math. Soc. 104 (1962) 278–283.

    MathSciNet  MATH  Google Scholar 

  11. J. Dixmier, "Les C*-algèbres et leurs représentations", Gauthier-Villars, Paris, 1964.

    MATH  Google Scholar 

  12. R.V. Kadison, "Transformations of states in operator theory and dynamics" Topology 3, Suppl. 2 (1965) 177–198.

    Article  MathSciNet  MATH  Google Scholar 

  13. G.W. Mackey, "Borel structure in groups and their duals", Trans. Amer. Math. Soc. 85 (1957) 134–165.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Narasimhan, "Analysis on Real and Complex Manifolds", North Holland, Amsterdam, 1968.

    MATH  Google Scholar 

  15. G.K. Pedersen, "C*-algebras and their Automorphism Groups", Academic Press, London-New York-San Francisco, 1979.

    MATH  Google Scholar 

  16. J. Peetre, "Rectification à l’article ‘Une caractérisation abstraite des opérateurs différentiels’", Math. Scand. 8 (1960) 116–120.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Huzihiro Araki Calvin C. Moore Şerban-Valentin Stratila Dan-Virgil Voiculescu

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verleg

About this paper

Cite this paper

Bratteli, O., Digernes, T., Elliott, G.A. (1985). Locality and differential operators on C*-algebras, II. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074879

Download citation

  • DOI: https://doi.org/10.1007/BFb0074879

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics