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Derivations and pure states

Published online by Cambridge University Press:  18 May 2009

J. P. Sproston
J. P. Sproston
Affiliation:
Department of Pure Mathematics, University of Hull, Hull
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In this note we point out and discuss a relationship between the following two properties which a C*-algebra A may have:

(D) all derivations on A are inner;

(P) the set of pure states of A is w*-compact.

The relationship is deduced from a comparison of two existing theorems ((I) and (II) below).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 73 - 77
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Akemann, C. A., Elliott, G. A., Pedersen, G. K. and Tomiyama, J., Derivations and multipliers of C*-algebras, to appear in Amer. J. Math.Google Scholar
2.Archbold, R. J., Certain properties of operator algebras (Ph.D. Thesis, University of Newcastle upon Tyne, 1972).Google Scholar
3.Dixmier, J., Les algèbres d'opérateurs dans l'espace Hilbertien (algèbres de von Neumann) (2nd edition, Gauthier-Villars, Paris, 1969).Google Scholar
4.Dixmier, J., Les C*-algèbres et leurs représentations (Gauthier-Villars, Paris, 1964;2nd edition 1969).Google Scholar
5.Elliott, G. A., Some C*-algebras with outer derivations, Rocky Mountain J. Math. 3 (1973), 501–506.CrossRefGoogle Scholar
6.Fell, J. M. G., The structure of algebras of operator fields, Acta Math. 106 (1961), 233–280.CrossRefGoogle Scholar
7.Glimm, J. G., On a certain class of operator algebras, Trans. Amer. Math. Soc. 95 (1960), 318–340.CrossRefGoogle Scholar
8.Glimm, J. G., Type I C*-algebras, Ann. of Math. 73 (1961), 572–612.CrossRefGoogle Scholar
9.Lance, E. C., Inner automorphisms of UHF algebras, J. London Math. Soc. 43 (1968), 681–688.CrossRefGoogle Scholar
10.Sakai, S., On some problems of C*-algebras, Tôhoku Math. J. 11 (1959), 453–455.CrossRefGoogle Scholar
11.Sakai, S., Derivations of simple C*-algebras, J. Functional Analysis 2 (1968), 202–206.CrossRefGoogle Scholar
12.Sproston, J. P., Derivations and automorphisms of homogeneous C*-algebras, Proc. London Math. Soc. (3) 32 (1976), 521–536.CrossRefGoogle Scholar
13.Tomiyama, J. and Takesaki, M., Applications of fibre bundles to the certain class of C*-algebras, Tôhoku Math. J. 13 (1961), 498–522.CrossRefGoogle Scholar