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The left Hilbert algebra associated to a semi-direct product*

Published online by Cambridge University Press:  24 October 2008

R. Rousseau
R. Rousseau
Affiliation:
Katholieke Universiteit, Leuven, Belgium
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Abstract

Let A and G be locally compact groups and α a continuous action of G on A, and let denote the semi-direct product of A and G. Then we prove that the left Hilbert algebra of continuous functions with compact support, has the same achieved left Hilbert algebra, as the crossed product of K(A)" by the associated action α̃ of G on . As a consequence we obtain that the canonical weight on is the dual weight of the canonical weight on K(A)".

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 3 , November 1977 , pp. 411 - 418
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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