Topics in Functional Analysis
AQFT and operator algebra
States and observables
Let be a von Neumann algebra acting on a Hilbert space .
A vector is a separating vector if implies for all .
The notions of separating vector is dual to that of cyclic vector with respect to the commutant , that is a vector is cyclic for iff it is separating for .
In the context of AQFT separating vectors appear as vacuum states . See Reeh-Schlieder theorem.
Revised on November 30, 2010 11:43:54
by Urs Schreiber