On the dimension theory of von Neumann algebras

• Autores: David Sherman
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 101, Nº 1, 2007, págs. 123-147
• Idioma: inglés
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• Resumen

  • 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 when M 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.