On some extension properties of von Neumann algebras

Abstract

1. In the theory of the structure of von Neumann algebras, a great deal of discussions has been devoted to the algebraic invariants. Recently, J. Schwartz [6], has shown a new behavior of the hyperfinite factor by introducing a new property, called property P, and proved the existence of new algebraic type of continuous finite factor. Very recently, one of the authors has proved that property P is an algebraic invariant [2] and it makes us to have some interest that the main results of the paper [6], especially the key results [6: Cor. 6 and Lemma 7], can be deducsd only from the point of view of the existence of a projection mapping of norm one.