Characterization of centralizers on nest subalgebras of von Neumann algebras by local action

Abstract

Let be a nest in an arbitrary factor von Neumann algebra . In this paper, it is proved that a linear local left (right) centralizer from the nest subalgebra into is a left (right) centralizer. Also, it is proved that a linear mapping from into itself is centralized at a given point if and only if is a centralizer.