## Abstract

We prove a generalized version of Powers’ averaging property that characterizes simplicity of reduced crossed products C(X) _{λ} G, where G is a countable discrete group, and X is a compact Hausdorff space which G acts on minimally by homeomorphisms. As a consequence, we generalize results of Hartman and Kalantar on unique stationarity to the state space of C(X) _{λ} G and to Kawabe’s generalized space of amenable subgroups Sub_{a}(X, G). This further lets us generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras. We prove that if C(Y ) ⊆ C(X) is an inclusion of unital commutative G-C*-algebras with X minimal and C(Y )_{λ}G simple, then any intermediate C*-algebra A satisfying C(Y ) _{λ} G ⊆ A ⊆ C(X) _{λ} G is simple.

Original language | English |
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Pages (from-to) | 2237-2254 |

Number of pages | 18 |

Journal | Transactions of the American Mathematical Society |

Volume | 375 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jan 2022 |

## Keywords

- C*-algebra
- Compact space
- Crossed product
- Group action
- Minimal
- Powers averaging property
- Simple