AW*-algebras Which are Enveloping C*-algebras of JC-algebras

In the given article, enveloping C*-algebras of AJW-algebras are considered. Conditions are given, when the enveloping C*-algebra of an AJW-algebra is an AW*-algebra, and corresponding theorems are proved. In particular, we proved that if $mathcal{A}$ is a real AW*-algebra, $mathcal{A}_{sa}$ is the JC-algebra of all self-adjoint elements of $mathcal{A}$ , $mathcal{A}+imathcal{A}$ is an AW*-algebra and $mathcal{A}cap imathcal{A} = {0}$ then the enveloping C*-algebra $C^*(mathcal{A}_{sa})$ of the JC-algebra $mathcal{A}_{sa}$ is an AW*-algebra. Moreover, if $mathcal{A}+imathcal{A}$ does not have nonzero direct summands of type I₂, then $C^*(mathcal{A}_{sa})$ coincides with the algebra $mathcal{A}+imathcal{A}$ , i.e. $C^*(mathcal{A}_{sa})= mathcal{A}+imathcal{A}$ .