Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T08:04:16.550Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivations on some (possibly non-separable) C*-algebras

Published online by Cambridge University Press:  18 May 2009

J. P. Sproston
J. P. Sproston
Affiliation:
Department of Pure Mathematics, University of Hull, 22/24, Newland Park, Cottingham Road, Hull, HU5 2DW.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In an important recent paper [4], G. A. Elliott has given a necessary and sufficient condition for every derivation on a separable C*-algebra with identity to be inner. Indeed, Elliott's condition has since been shown, by Akemann and Pedersen, to be equivalent to the C*-algebra being a finite direct sum of C*-algebras which are either homogeneous of finite degree or simple [8, Corollary 3.10].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 43 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Dixmier, J., Les algèbres d'opérateurs dans l'espace Hilbertien (Algébres de von Neumann), 2nd edition (Gauthier-Villars, 1969).Google Scholar
2.Dixmier, J., Les C-algèbres et lews représentations, 2nd edition (Gauthier-Villars, 1969).Google Scholar
3.Elliott, G. A., Some C-algebras with outer derivations, Rocky Mountain J. Math. 3 (1973), 501–506.CrossRefGoogle Scholar
4.Elliott, G. A., Some C-algebras with outer derivations, III, Ann. of Math. 106 (1977), 121–143.CrossRefGoogle Scholar
5.Fell, J. M. G., The structure of algebras of operator fields, Ada Math. 106 (1961), 233–280.Google Scholar
6.Sproston, J. P., Derivations and automorphisms of homogeneous C-algebras, Proc. London Math. Soc. (3) 32 (1976), 521–536.Google Scholar
7.Vasil'ev, N. B., C-algebras with finite-dimensional irreducible representations, Russian Math. Surveys 21 (1966), 137–155.CrossRefGoogle Scholar
8.Akemann, C. A. and Pedersen, G. K., Central sequences and inner derivations of separable C-algebras, Amer. J. Math. 101 (1979), 1047–1061.CrossRefGoogle Scholar