On the amenability of partial and enveloping actions

Details On the amenability of partial and enveloping actions On the amenability of partial and enveloping actions

2009-06-08

arxiv.org/abs/0906.1562v1

Mathematics

Operator Algebras

5 pages, to appear in the Proc. of the AMS

Scientific paper

We prove that a partial action is amenable if and only if so is its Morita
enveloping action. As applications we prove that any partial representation of
a discrete group is positive definite, and we extend a result of Zeller-Meier
concerning the amenability of discrete groups and the existence of invariant
states to partial actions.

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