Editing Noncommutative geometry (section)

==Noncommutative C*-algebras, von Neumann algebras==
The (formal) duals of [[non-commutative]] [[C*-algebra]]s are often now called non-commutative spaces. This is by analogy with the [[Gelfand representation]], which shows that [[commutative]] C*-algebras are [[Duality (mathematics)|dual]] to [[locally compact]] [[Hausdorff space]]s.  In general, one can associate to any C*-algebra ''S'' a topological space ''Ŝ''; see [[spectrum of a C*-algebra]].

For the [[duality (mathematics)|duality]] between localizable [[measure space]]s and commutative [[von Neumann algebra]]s, [[noncommutative]] [[von Neumann algebra]]s are called ''non-commutative [[measure space]]s''.