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 cyclic vector if is dense in .
The notions of cyclic vector is dual to that of separating vector with respect to the commutant , that is a vector is cyclic for iff it is separating for .
In the context of AQFT cyclic vector appear as vacuum states . See Reeh-Schlieder theorem.
Revised on November 30, 2010 11:42:37
by Urs Schreiber