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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On special generators for properly infinite von Neumann algebras


Author: W. R. Wogen
Journal: Proc. Amer. Math. Soc. 28 (1971), 107-113
MSC: Primary 46.65; Secondary 47.00
MathSciNet review: 0276790
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0276790-X
PII: S 0002-9939(1971)0276790-X
Keywords: Generator, properly infinite von Neumann algebra, hyponormal, transcendental quasinilpotent, unimodular contraction
Article copyright: © Copyright 1971 American Mathematical Society