Generators of von~Neumann algebras associated with spectral measures

Details Generators of von~Neumann algebras associated with spectral measures Generators of von~Neumann algebras associated with spectral measures

2011-11-24

arxiv.org/abs/1111.5847v1

Mathematics

Operator Algebras

9 pages. arXiv admin note: substantial text overlap with arXiv:1012.2588

Scientific paper

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.

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