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 all vectors ξ,η∈H, coefficient function u↦⟨uxu∗ξ|η⟩ weakly almost periodic topological group UM of unitaries in (equipped with weak operator topology). The main device unique invariant mean C∗-algebra WAP(UM) functions UM. Next, we direct sum diffuse, abel...

Let G be a locally compact group, and consider the weakly-almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C∗-subalgebra of the commutative C∗-algebra M(G)∗, and so has character space, say K. In this paper, we investigate properties of K. We present two proofs, one using tensor product techniques, and the other using vector-valued integration, to s...

0