Almost and weakly almost periodic functions on the unitary groups of von Neumann algebras
Almost and weakly almost periodic functions on the unitary groups of von Neumann algebras
Let M⊂B(H) be a von Neumann algebra acting on the (separable) Hilbert space H. We first prove that M is finite if and only if, for every x∈M and for all vectors ξ,η∈H, the coefficient function u↦⟨uxu∗ξ|η⟩ is weakly almost periodic on the topological group UM of unitaries in M …