Extension of Dixmier's approximation theorem to tau-measurable operators affiliated with type IIinfinity von Neumann algebras

Abstract: 

The classical result of the Dixmier approximation theorem states that the centre of a von Neumann algebra has a nonempty intersection with the norm-closure of the convex hull of every unitary orbit. The result still holds under the measure topology for operators in the symmetric space (L1+L∞)(M,T) when M is a type II∞ von Neumann algebra equipped with a semi-finite normal faithful trace T. Moreover, we find that under the local measure topology the space S(M,T) also satisfies Dixmier's original result.