User:Nsoum/sandbox/Finite von Neumann algebras
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References
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In mathematics, a finite von Neumann algebra is a von Neumann algebra whose identity element is a finite projection i.e. the identity is not Murray-von Neumann equivalent to a proper subprojection in the von Neumann algebra. A defining feature of these von Neumann algebras is the existence of a unique center-valued trace.
Definition
[edit]Let N ⊆ B(H) be a von Neumann algebra with center Z. We say that N is finite if for any two Murray-von Neumann equivalent projections p, q in N such that q ≤ p, we have that p = q.
Examples
[edit]Abelian von Neumann algebras
[edit]Finite-dimensional von Neumann algebras
[edit]II_1 factors
[edit]Center-valued Trace
[edit]Representation
[edit]Let τ