On the dimension theory of von Neumann algebras
Operator Algebras
2007-05-23 v1 Functional Analysis
Abstract
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 sigma-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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Cite
@article{arxiv.math/0503747,
title = {On the dimension theory of von Neumann algebras},
author = {David Sherman},
journal= {arXiv preprint arXiv:math/0503747},
year = {2007}
}
Comments
24 pages