On topological properties of orthogonal vector fields

Description of orthogonal vector fields over W*-algebra of type I 2

“…If a linear map F with the property (3) is continuous in w * -topology on A and weak topology on H, then the map F is referred to as w * -continuous OVF. It should be noted that a w * -continuous OVF F is bounded, so that it is an OVF [7,Corollary 3]. A w * -continuous OVF F is said to be stationary [3], if there exist two functionals ϕ, ψ ∈ A + * such that…”

“…Equality ( 6) follows from the spectral theorem with regard to (3), and the following computation gives (7):…”