Abstract: 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.
For citation: Ayupov S. A., Arzikulov F. N. Reversible AJW-algebras // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 19, no. 3, pp. 15-21.
DOI 10.23671/VNC.2016.3.5872
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