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Transitive families of projections in factors of type $II_{1}$


Author: Jon P. Bannon
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
Published electronically: October 7, 2004
MathSciNet review: 2113934
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Abstract | References | Similar Articles | Additional Information

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 $II_{1}$.


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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

DOI: https://doi.org/10.1090/S0002-9939-04-07717-2
Keywords: II$_{1}$ factor, transitive family, free product
Received by editor(s): November 18, 2003
Published electronically: October 7, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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