On the Mackey Borel structure

Let A be a C *-algebra and a Hilbert space which is infinite dimensional and of Hilbert dimension ≧ dim π for all π ∈ Â. Suppose that the set Irr of all non-null *-representations π of A on , irreducible on the essential space , is given the relative strong topology as a subspace of Rep [2; 4; 6]. That is, the topology is that of simple convergence in with the strong topology. Finally, let ∼ denote equivalence of representations in Irr implemented by partial isometries in if and only if there exists a partial isometry with vv * ⊃ H(π 1) and v * v ⊃ H(π 2) satisfying π 2(a) = v*π 1(a)v for all a ∈ A

Английский

Canadian Journal of Mathematics. – 1971. – Vol. 23, № 4. – P. 674–678.