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Transitive families of projections in factors of type  |
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| Authors: | Jon P Bannon |
| Institution: | Department of Mathematics and Statistics, The University of New Hampshire, Dur- ham, New Hampshire 03872 |
| 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  . |
| Keywords: | II$_{1}$ factor transitive family free product |
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