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Discontinuous homomorphisms from C*-algebras

Published online by Cambridge University Press:  24 October 2008

D. W. B. Somerset
D. W. B. Somerset
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT
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Abstract

A necessary and sufficient condition is given for a unital C*-algebra A to admit a discontinuous homomorphism into a Banach algebra which is continuous on its centre. The condition is that A must have a Glimm ideal G such that the C*-algebra A/G admits a discontinuous homomorphism into a Banach algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 147 - 150
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Albrecht, E. and Dales, H. G.. Continuity of homomorphisms from C*-algebras and other Banach algebras. In Proc. of the Long Beach Conference on Radical Banach Algebras and Automatic Continuity, Lecture Notes in Math. vol. 975 (Springer-Verlag, 1983), pp. 375–396.CrossRefGoogle Scholar
[2]Archbold, R. J.. Density theorems for the centre of a C*-algebra. J. London Math. Soc. (2) 10 (1975), 189–197.CrossRefGoogle Scholar
[3]Archbold, R. J. and Somerset, D. W. B.. Quasi-standard C*-algebras. Math. Proc. Cambridge Philos. Soc. 107 (1990), 349–360.CrossRefGoogle Scholar
[4]Cleveland, S. B.. Homomorphisms of non-commutative *-algebras. Pacific J. Math. 13 (1963), 1097–1109.CrossRefGoogle Scholar
[5]Dales, H. G.. A discontinuous homomorphism from C(X). Amer. J. Math. 101 (1979), 647–734.CrossRefGoogle Scholar
[6]Dales, H. G. and Woodin, W. H.. An Introduction to Independence for Analysts. London Math. Soc. Lecture Note Series no. 115 (Cambridge University Press, 1987).CrossRefGoogle Scholar
[7]Estrele, J.. Semi-normes sur C(K). Proc. London Math. Soc. (3) 36 (1978), 27–45.CrossRefGoogle Scholar
[8]Glimm, J.. A Stone-Weierstrass theorem for C*-algebras. Ann. of Math. 72 (1960), 216–244.CrossRefGoogle Scholar
[9]Johnson, B. E.. The uniqueness of the (complete) norm topology. Bull. Amer. Math. Soc. 73 (1967), 537–541.CrossRefGoogle Scholar
[10]Johnson, B. E.. Continuity of homomorphisms of algebras of operators II. J. London Math. Soc. (2) 1 (1969), 81–84.CrossRefGoogle Scholar
[11]Laursen, K. B.. Central factorization in C*-algebras and continuity of homomorphisms. J. London Math. Soc. (2) 28 (1983), 123–130.CrossRefGoogle Scholar
[12]Laursen, K. B.. Central factorization in C*-algebras and its use in automatic continuity. Contemp. Math. 32 (1984), 169–176.CrossRefGoogle Scholar
[13]Sinclair, A. M.. Homomorphisms from C*-algebras. Proc. London Math. Soc. (3) 29 (1974), 435–452CrossRefGoogle Scholar
Sinclair, A. M.. Corrigendum Proc. London Math. Soc. 32 (1976), 322.CrossRefGoogle Scholar
[14]Wright, F. B.. A reduction theory for algebras of finite type. Ann. of Math. 60 (1954), 560–570.CrossRefGoogle Scholar