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.)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Albrecht and M. Neumann, "Local operators between spaces of ultradifferentiable functions and ultradistributions", Manuscripta Math. 38 (1982) 131–161.
C.J.K. Batty, "Derivations on compact spaces", Proc. London Math. Soc. (3) 42 (1981) 299–330.
C.J.K. Batty, "Local operators and derivations on C*-algebras", preliminary version (1983).
O. Bratteli, T. Digernes, and D.W. Robinson, "Relative locality of derivations", preprint (1983).
O. Bratteli, G.A. Elliott, and D.E. Evans, "Locality and differential operators on C*-algebras", preprint (1983).
O. Bratteli, F. Goodman, and P.E.T. Jørgensen, "Unbounded derivations tangential to compact groups of automorphisms II", preprint (1983).
O. Bratteli and P.E.T. Jørgensen, "Unbounded derivations tangential to compact groups of automorphisms", J. Functional Analysis 48 (1982) 107–133.
O. Bratteli and D.W. Robinson, "Operator algebras and quantum statistical mechanics, I and II", Springer-Verlag, Berlin-Heidelberg-New York, 1979 and 1981.
C. Davis, "The Toeplitz-Hausdorff theorem explained", Canad. Math. Bull. 14 (1971) 245–246.
J. Dixmier, "Dual et quasi-dual d’une algèbre de Banach involutive" Trans. Amer. Math. Soc. 104 (1962) 278–283.
J. Dixmier, "Les C*-algèbres et leurs représentations", Gauthier-Villars, Paris, 1964.
R.V. Kadison, "Transformations of states in operator theory and dynamics" Topology 3, Suppl. 2 (1965) 177–198.
G.W. Mackey, "Borel structure in groups and their duals", Trans. Amer. Math. Soc. 85 (1957) 134–165.
R. Narasimhan, "Analysis on Real and Complex Manifolds", North Holland, Amsterdam, 1968.
G.K. Pedersen, "C*-algebras and their Automorphism Groups", Academic Press, London-New York-San Francisco, 1979.
J. Peetre, "Rectification à l’article ‘Une caractérisation abstraite des opérateurs différentiels’", Math. Scand. 8 (1960) 116–120.
Author information
Authors and Affiliations
Editor information
Rights 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