Editing Von Neumann algebra (section)

== Commutative von Neumann algebras ==
{{Main|Abelian von Neumann algebra}}

The relationship between [[commutative]] von Neumann algebras and [[measure space]]s is analogous to that between commutative [[C*-algebra]]s and [[locally compact]] [[Hausdorff space]]s.  Every commutative von Neumann algebra is isomorphic to [[Lp space|''L''<sup>∞</sup>]](''X'') for some measure space (''X'', μ) and conversely, for every σ-finite measure space ''X'', the *-algebra ''L''<sup>∞</sup>(''X'') is a von Neumann algebra.

Due to this analogy, the theory of von Neumann algebras has been called noncommutative measure theory, while the theory of [[C*-algebra]]s is sometimes called [[noncommutative topology]] {{harv|Connes|1994}}.