On special generators for properly infinite von Neumann algebras
HTML articles powered by AMS MathViewer
- 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.References
-
H. Behncke, Generators of ${W^ \ast }$-algebras (to appear).
- Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
- Carl Pearcy, On certain von Neumann algebras which are generated by partial isometries, Proc. Amer. Math. Soc. 15 (1964), 393–395. MR 161172, DOI 10.1090/S0002-9939-1964-0161172-8
- Bernard Russo, Unimodular contractions in Hilbert space, Pacific J. Math. 26 (1968), 163–169. MR 231214
- David M. Topping, Transcendental quasi-nilpotents in operator algebras, J. Functional Analysis 2 (1968), 342–351. MR 0233212, DOI 10.1016/0022-1236(68)90011-6 —, Lectures on von Neumann algebras, Lecture notes, Tulane University, 1969.
- Warren Wogen, On generators for von Neumann algebras, Bull. Amer. Math. Soc. 75 (1969), 95–99. MR 236725, DOI 10.1090/S0002-9904-1969-12157-9
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