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On L1-kernels of unitary representations of semisimple Lie groups

Published online by Cambridge University Press:  24 October 2008

Mohammed E. B. Bekka  and
Jean Ludwig
Mohammed E. B. Bekka
Affiliation:
Institut de Mathématiques, Université de Lausanne, CH-1015 Lausanne, Suisse
Jean Ludwig
Affiliation:
Département de Mathématiques et Informatique, Université de Metz, Ile du Saulcy, JF-57045 Metz, France
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Extract

Let G be a locally compact group with fixed left Haar measure dx. Recall that G is said to be amenable if there exists a left translation invariant mean on the space L∞(G), i.e. if there exists a positive, linear functional M on L∞(G) such that M(lG) = 1 and M(xø) = Mø for all ø∈L∞(G), x∈G, where xø denotes the left translate xø(y) = ø(xy). The class of amenable groups includes all soluble and all compact groups (concerning the theory of amenable groups we refer to [9]). It is easy to see that G is amenable if and only if ℂ1G, the space of the constant functions on G, has a closed left translationinvariant complement in L∞(G). This reformulation of amenability leads to the following more general question.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 343 - 348
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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