On Two Problems Concerning Enveloping von Neumann Algebras of JW-Algebras

Abstract

In the given article, we have given a new proof of the result: a reversible JC-algebra is a JW-algebra if and only if the enveloping C*-algebra of this JC-algebra is a von Neumann algebra. Also we have given a characterization of all extensions to measure of an arbitrary measure, defined on projections of a reversible JW-algebra with no type I 2 direct summand.