Geodesic
Reversible AJW-algebras
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 15-21

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The main result states that every special AJW-algebra can be decomposed into the direct sum of totally irreversible and reversible subalgebras. In turn, every reversible special AJW-algebra decomposes into a direct sum of two subalgebras, one of which has purely real enveloping real von Neumann algebra, and the second one contains an ideal, whose complexification is a C$^*$-algebra and the annihilator of this complexification in the enveloping $C^*$-algebra of this subalgebra is equal to zero. 
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     author = {Sh. A. Ayupov and F. N. Arzikulov},
     title = {Reversible {AJW-algebras}},
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Sh. A. Ayupov; F. N. Arzikulov. Reversible AJW-algebras. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 3, pp. 15-21. http://geodesic.mathdoc.fr/item/VMJ_2016_18_3_a1/