MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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 '10 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 '10 at 7:23
Yes I mente discrete group. Sorry – m07kl Oct 16 '10 at 8:40
up vote 3 down vote accepted

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.

share|cite|improve this answer
Thanks for reference – m07kl Oct 16 '10 at 8:35
I think this is more easier to see if we use definition in [2] Section 4.3. – m07kl Oct 16 '10 at 8:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.