Intermediate subalgebras of cross-product von Neumann algebras arising from weakly compact actions

In this short paper, we establish the following Galois-type property for all measure-preserving, weakly compact actions $G \curvearrowright (X,μ) $ of a non-inner amenable group $G$ on a standard probability space $X$: for any intermediate von Neumann subalgebra $\mathcal L(G)\subseteq \mathcal N \s