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DOI: 10.23671/VNC.2016.3.5872

# Reversible AJW-algebras

Ayupov S. A. , Arzikulov F. N.
Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 3.
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.
Keywords: AJW-algebra, reversible AJW-algebra, AW$^*$-algebra, Enveloping $$C^*$$-algebra
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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