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

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

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

Bannon, Jon P.

Proceedings of the American Mathematical Society, 03/2005, Volume: 133, Issue: 3

Journal Article

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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Bannon, Jon P.

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