THE DISTANCE FORMULA FOR THE DERIVATION PROBLEM

Abstract

In this paper we discuss questions related to the perturbation of von Neumann algebras. We will show that the distance between an arbitrary operator of M and the commutant M' is the same as the distance from the same operator to the trivial center CI of M where M is a type II-factor in a separable Hilbert space. As a consequence, the derivation implemented by some element x is an element of M has the same norm as the distance from x to the commutant M'.