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Locality and differential operators on C*-algebras, II

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

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.)

Keywords

  • Density Matrix
  • Vector State
  • Irreducible Representation
  • Pure State
  • Additional Hypothesis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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 

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© 1985 Springer-Verleg

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15643-7

  • Online ISBN: 978-3-540-39514-0

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