Transitive families of projections in factors of type $II_{1}$
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Abstract:
We introduce a notion of transitive family of subspaces relative to a type $II_{1}$ factor, and hence a notion of transitive family of projections in such a factor. We show that whenever $\mathcal {M}$ is a factor of type $II_{1}$ and $\mathcal {M}$ is generated by two self-adjoint elements, then $\mathcal {M}\otimes M_{2}(\mathbb {C})$ contains a transitive family of $5$ projections. Finally, we exhibit a free transitive family of $12$ projections that generate a factor of type $II_{1}$.References
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Additional Information
- Jon P. Bannon
- Affiliation: Department of Mathematics and Statistics, The University of New Hampshire, Dur- ham, New Hampshire 03872
- Email: jpbannon@math.unh.edu
- Received by editor(s): November 18, 2003
- Published electronically: October 7, 2004
- Communicated by: David R. Larson
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 835-840
- MSC (2000): Primary 46L54; Secondary 47A62
- DOI: https://doi.org/10.1090/S0002-9939-04-07717-2
- MathSciNet review: 2113934