Transitive Families of Projections in Factors of Type II1

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Transitive Families of Projections in Factors of Type II1

BANNON, Jon P

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

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We introduce a notion of transitive family of subspaces relative to a type II1factor, and hence a notion of transitive family of projections in such a factor. We show that whenever M is a factor of type II1and 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 II1.

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BANNON, Jon P

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