On the Dimension Theory of Von Neumann Algebras
نویسنده
چکیده
In this paper we study three aspects of (P(M)/ ∼), the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra M. First we determine the topological structure that (P(M)/ ∼) inherits from the operator topologies on M. Then we show that there is a version of the center-valued trace which extends the dimension function, even whenM is not σ-finite. Finally we prove that (P(M)/ ∼) is a complete lattice, a fact which has an interesting reformulation in terms of representations.
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