Type II factor; distance of two C*-algebras; derivation
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, v. 46, NO 4, Page. 489-494
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'.