On special generators for properly infinite von Neumann algebras

Wogen, W. R.

doi:10.1090/S0002-9939-1971-0276790-X

On special generators for properly infinite von Neumann algebras
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by W. R. Wogen

Proc. Amer. Math. Soc. 28 (1971), 107-113

DOI: https://doi.org/10.1090/S0002-9939-1971-0276790-X

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Abstract:

It is known that every properly infinite von Neumann algebra $\mathcal {A}$ on a separable Hilbert space has a single generator. We show in this paper that a generator for $\mathcal {A}$ may be chosen from some special classes of operators. In particular each of the following classes of operators contains a generator for $\mathcal {A}$: the hyponormals, the nilpotents, the transcendental quasinilpotents, and the unimodular contractions. We also show that a generator for $\mathcal {A}$ may be chosen with arbitrarily prescribed spectrum.

References

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