Inner amenability and fullness

Choda, Marie

doi:10.1090/S0002-9939-1982-0674101-6

Inner amenability and fullness
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Proc. Amer. Math. Soc. 86 (1982), 663-666 Request permission

Abstract:

Let $G$ be a countable group which is not inner amenable. Then the II$_{1}$-factor $M$ is full in the following cases: (1) $M$ is given by the group measure space construction from a triple $(X,\mu ,G)$ with respect to a strongly ergodic measure preserving action of $G$ on a probability space $(X,\mu )$. (2) $M$ is the crossed product of a full II$_{1}$-factor by $G$ with respect to an action.

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