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arXiv · 1111.5847

Generators of von Neumann algebras associated with spectral measures

A. G. Smirnov
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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.

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BibTeXRIS

A. G. Smirnov. 2011-11-24. Generators of von Neumann algebras associated with spectral measures. https://doi.org/10.1016/j.jmaa.2012.08.066

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