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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On special generators for properly infinite von Neumann algebras
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by W. R. Wogen PDF
Proc. Amer. Math. Soc. 28 (1971), 107-113 Request permission

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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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 107-113
  • MSC: Primary 46.65; Secondary 47.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0276790-X
  • MathSciNet review: 0276790