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Is every action from an amenable group amenable on a unital $C^*$-algebra?

flag	asked Oct 15 2010 at 20:01 m07kl 551●3●8

It would help if you reminded people what you mean by an amenable action on a $C^*$-algebra, and made more precise the quantifiers in your question. – Yemon Choi Oct 16 2010 at 4:33

Ah, so you were asking if each (discrete?) amenable group has an amenable action on some unital C*-algebra. This seems to be answered below. – Yemon Choi Oct 16 2010 at 7:23

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Yes I mente discrete group. Sorry – m07kl Oct 16 2010 at 8:40

Makoto Yamashita · Accepted Answer · 2010-10-16 06:37:28Z UTC

Yes it is. It follows from Theorem 3.3 of [1] and the fact that the trivial action of an amenable group on $\mathbb{C}$ is amenable. More modern reference is [2] (in particular Section 4.3).

[1] C. Anantharaman-Delaroche. Systèmes dynamiques non commutatifs et moyennabilité. Math. Ann., 279(2):297–315, 1987.

[2] N. P. Brown and N. Ozawa. C*-algebras and finite-dimensional approximations, volume 88 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2008.

Is every action from an amenable group amenable on a unital $C^*$-algebra?

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