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Amenability of Lipschitz algebras

Published online by Cambridge University Press:  24 October 2008

Frédéric Gourdeau
Frédéric Gourdeau
Affiliation:
Département de Mathématiques et de Statistiques, Cité Universitaire, Québec, Canada GlK 7P4
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Extract

In this article, we study the amenability of Banach algebras in general, and that of Lipschitz algebras in particular. After introducing an alternative definition of amenability, we extend a result of [5], thereby proving a new characterization of amenability for Banach algebras. This characterization relates the amenability of a Banach algebra A to the space of bounded homomorphisms from A into another Banach algebra B (Theorem 4). This result allows us to solve the problem of amenability for virtually all Lipschitz algebras (of complex or Banach algebra valued functions), a class of algebras which has been studied in [2], [4] and [5].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 581 - 588
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

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