Transitive families of projections in factors of type

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 factor, and hence a notion of transitive family of projections in such a factor. We show that whenever is a factor of type and is generated by two self-adjoint elements, then contains a transitive family of projections. Finally, we exhibit a free transitive family of projections that generate a factor of type .

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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.