Abstract
Let (X, Γ) be a free minimal dynamical system, where X is a compact separable Hausdorff space and Γ is a discrete amenable group. It is shown that, if (X, Γ) has a version of Rokhlin property (uniform Rokhlin property) and if C(X) ⋊ Γ has a Cuntz comparison on open sets, then the comparison radius of the crossed product C*-algebra C(X) ⋊ Γ is at most half of the mean topological dimension of (X, Γ).These two conditions are shown to be satisfied if Γ = ℤ or if (X, Γ) is an extension of a free Cantor system and Γ has subexponential growth. The main tools being used are Cuntz comparison of diagonal elements of a subhomogeneous C*-algebra and small subgroupoids.
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