Reversible AJW-algebras

Abstract

In this article it is proved that for every special AJW-algebra $A$ there exist central projections $e$, $f$, $g\in A$, $e+f+g=1$ such that (1) $eA$ is reversible and there exists a norm-closed two sided ideal $I$ of $C^{\ast }(eA)$ such that $eA={}^{\perp }{(}^{\perp }(I_{sa}{)}_{+}{)}_{+}$; (2) $fA$ is reversible and $R^{\ast }(fA)\cap i{R}^{\ast }(fA)=\{0\}$; (3) $gA$ is a totally nonreversible AJW-algebra.

7 pages