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The characterization of differential operators by locality: abstract derivations

Published online by Cambridge University Press:  19 September 2008

C. J. K. Batty  and
D. W. Robinson
C. J. K. Batty
Affiliation:
Department of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, Scotland
D. W. Robinson
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia
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Abstract

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Let δ be a closed *-derivation on a commutative C*-algebra , suppose that is dense in for some n = 1, 2, …, ∞, and let be a linear operator satisfying the locality condition

It is shown that , for some finite integer p≤n and functions lm on X. Estimates on the coefficients lm are obtained and applied to flows and local flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 171 - 183
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Batty, C. J. K.. Derivations on compact spaces. Proc. London Math. Soc. 42 (1981), 299–330.Google Scholar
[2]Batty, C. J. K.. Derivations of abelian C*-algebras. Proc. Symp. Pure Math. 38 (1982) part 2, 333–338.Google Scholar
[3]Bratteli, O., Elliott, G. A. & Robinson, D. W.. The characterization of differential operators by locality: classical flows. Trondheim preprint (1984).Google Scholar
[4]Davies, E. B.. One-parameter Semigroups. Academic Press, (1980).Google Scholar
[5]Johnson, B. E.. Continuity of derivations on commutative algebras. Amer. J. Math. 91 (1969), 1–10.Google Scholar
[6]Peetre, J.. Une caractérisation abstraite des opérateurs différentiels. Math. Scand. 7 (1959), 211–218.;Google Scholar
and Rectification à l'article précédent. Math. Scand. 8 (1960), 116–120.Google Scholar
[7]Rubel, L. A., Squires, W. A. & Taylor, B. A.. Irreducibility of certain entire functions with applications to harmonic analysis. Ann. Math. 108 (1978), 553–567.Google Scholar