Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators

Abstract

Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ We describe class of von Neumann algebras $M$ for which the algebra $E(M)$ coincides with the algebra $S(M)$ -- the algebra of all measurable operators with respect to $M,$ and with $S(M, \tau)$ -- the algebra of all $\tau$-measurable operators with respect to $M.$