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Let $\Gamma$ be a discrete group and $A$ be a $C^*$-algebra. Consider an action $\alpha: \Gamma \to \operatorname{Aut}(A)$. There is a notion of amenability for such an action (see e.g. Brown and Ozawa's book "C*-algebras and finite-dimensional approximations", section 4.3), but how should one think intuitively about an amenable action? How was it motivated?

Let $\Gamma$ be a discrete group and $A$ be a $C^*$-algebra. Consider an action $\alpha: \Gamma \to \operatorname{Aut}(A)$. There is a notion of amenability for such an action (see e.g. Brown and Ozawa's book "C*-algebras and finite-dimensional approximations", section 4.3), but how should one think intuitively about an amenable action? How was the definition originally motivated?

Let $\Gamma$ be a discrete group and $A$ be a $C^*$-algebra. Consider an action $\alpha: \Gamma \to \operatorname{Aut}(A)$. There is a notion of amenability for such an action, but how should one think intuitively about an amenable action? How was it motivated?

Let $\Gamma$ be a discrete group and $A$ be a $C^*$-algebra. Consider an action $\alpha: \Gamma \to \operatorname{Aut}(A)$. There is a notion of amenability for such an action (see e.g. Brown and Ozawa's book "C*-algebras and finite-dimensional approximations", section 4.3), but how should one think intuitively about an amenable action? How was it motivated?