(o)-Topology in *-algebras of locally measurable operators - Muratov, M. A.; Chilin, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We consider the topology \( t( M ) \) of convergence locally in measure in the *-algebra \( LS( M ) \) of all locally measurable operators affiliated to the von Neumann algebra \( M \). We prove that \( t( M ) \) coincides with the (o)-topology in \( LS_h( M ) = { T LS( M ):T* = T } \) if and only if the algebra \( M \) is σ-finite and is of finite type. We also establish relations between \( t( M ) \) and various topologies generated by a faithful normal semifinite trace on \( M \).