Generators of von Neumann algebras associated with spectral measures

Abstract

Let $P_E$ be the set of all values of a spectral measure $E$ and $A(P_E)$ be the smallest von Neumann algebra containing $P_E$. We give a simple description of all sets of generators of $A(P_E)$ in terms of the integrals with respect to $E$. The treatment covers not only the case of generators belonging to $A(P_E)$, but also the case of (possibly unbounded) generators affiliated with this algebra.