This is not a Wikipedia article: It is an individual user's work-in-progress page, and may be incomplete and/or unreliable. For guidance on developing this draft, see Wikipedia:So you made a userspace draft. Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
New article name goes here new article content ...
References
editExternal links
edit
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
editLet 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
editAbelian von Neumann algebras
editFinite-dimensional von Neumann algebras
editII_1 factors
editCenter-valued Trace
editRepresentation
editLet τ