Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: October 7, 2004
MathSciNet review: 2113934
Full-text PDF Free Access

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 $II_{1}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L54, 47A62

Retrieve articles in all journals with MSC (2000): 46L54, 47A62


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: http://dx.doi.org/10.1090/S0002-9939-04-07717-2
PII: S 0002-9939(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.