Geometry and the Jones projection of a state

ANDRUCHOW, ESTEBAN; VARELA, ALEJANDRO

INTEGRAL EQUATIONS AND OPERATOR THEORY

BIRKHAUSER VERLAG AG

Lugar: Berna; Año: 1996 vol. 25 p. 129 - 146

0378-620X

Let A be a von Neumann algebra and φ a faithful normal state. Then O ϕ = {ϕ º Ad(g -1) : g ∈G A } and U ϕ = {ϕ º Ad(u *) : u ∈U A } are homogeneous reductive spaces. IfA is a C * algebra, e φ the Jones projection of the faithful state φ viewed as a conditional expectation, then we prove that the similarity orbit of  eφ by invertible elements of A can be imbedded in A⊗A in such a way thate ϕ is carried to 1 ⊗ 1 and the orbit of eφ to a homogeneous reductive space and an analytic submanifold of A⊗A.