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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 3, Pages 15–21 (Mi vmj585)  

This article is cited in 1 scientific paper (total in 1 paper)

Reversible AJW-algebras

Sh. A. Ayupova, F. N. Arzikulovb

a National University of Uzbekistan, Institute of Math., Do'rmon yo'li st., Tashkent, 1000125, UZBEKISTAN
b Andizhan State University, Department of Mathematics, University street, Andizhan, 710020, UZBEKISTAN

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.

Key words: AJW-algebra, reversible AJW-algebra, AW$^*$-algebra, enveloping $C^*$-algebra.

Full text: PDF file (207 kB)
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UDC: 517.98
MSC: 17C65, 46L57
Received: 24.09.2015
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Citation: Sh. A. Ayupov, F. N. Arzikulov, “Reversible AJW-algebras”, Vladikavkaz. Mat. Zh., 18:3 (2016), 15–21

Citation in format AMSBIB
\Bibitem{AyuArz16}
\by Sh.~A.~Ayupov, F.~N.~Arzikulov
\paper Reversible AJW-algebras
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 3
\pages 15--21
\mathnet{http://mi.mathnet.ru/vmj585}


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    This publication is cited in the following articles:
    1. S. Pulmannova, “Corrigendum to Banach synaptic algebras”, Int. J. Theor. Phys., 57:12 (2018), 3772–3775  crossref  mathscinet  zmath  isi  scopus
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