The Bost conjecture, open subgroups and groups acting on trees

摘要

We prove that the Bost conjecture with C*-algebra coefficients for locally compact Hausdorff groups passes to open subgroups. We also prove that if a locally compact Hausdorff group acts oil a free, then the Bost conjecture with C*-coefficients is true for the group if and only if it is true for the stabilisers of, the vertices.