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Discontinuous homomorphisms from Banach *-algebras

Published online by Cambridge University Press:  24 October 2008

Volker Runde
Volker Runde
Affiliation:
Fachbereich 9 Mathematik, Universität des Saarlandes, Postfach 151150, 66041 Saarbrücken, Germany e-mail: runde@math.uni-sb.de
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The long open problem raised by I. Kaplansky if, for an infinite compact Hausdorff space X, there is a discontinuous homomorphism from (X) into a Banach algebra was settled in the 1970s, independently, by H. G. Dales and J. Esterle. If the continuum hypothesis is assumed, then there is a discontinuous homomorphism from (X) (see [8] for a survey of both approaches and [9] for a unified exposition). The techniques developed by Dales and Esterle are powerful enough to yield discontinuous homomorphisms from commutative Banach algebras other than (X). In fact, every commutative Banach algebra with infinitely many characters is the domain of a discontinuous homomorphism ([7]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 4 , November 1996 , pp. 703 - 708
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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