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



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


