Reversible AJW-algebras

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	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 Language: Russian Download the full text 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 + References 1. Albeverio S., Ayupov Sh. A. and Abduvaitov A. H. On Real AW-algebras. Methods of Functional Analysis and Topology, 2005. vol. 11, no. 2, pp. 99-112. 2. Albeverio S., Ayupov Sh. A. and Abduvaitov A. H. On the coincidence of types of a real AW-algebra and its comlexification // News of Russian Acad. of Sci. Math. ser., 2004, vol. 68, pp. 3-12. [Russian]. 3. Arzikulov F. N. On abstract JW-algebras // Sib. Math. J., 1998, vol. 39, pp. 20-27. 4. Arzikulov F. N. On an analog of the Peirce decomposition // Sib. Math. J., 1999, vol. 40, pp. 413-419. 5. Arzikulov F. N. AJW-algebras of type I and their classification // Sib. Adv. Math., 1998, vol. 8, pp. 30-48. 6. Ayupov Sh. A. Traces on JW-algebras and enveloping \(W^{\ast}\)-algebras // Math. Z., 1987, vol. 194, pp. 15-23. 7. Ayupov Sh. Classification and representation of ordered Jordan algebras Fan. Tashkent, 1986. [Russian]. 8. Chilin V. I. Partial ordered Baer involutive algebras // Sovrem. Problemy Matematiki, Itogi nauki i tehkniki. VINITI, 1985, vol. 27, pp. 99-128 [Russian]. 9. Hanche-Olcen H., Stormer E. Jordan Operator Algebras. Boston etc: Pitman Publ. Inc., 1984. 10. Kusraev A. G. On the structure of AJW-algebras of type \(I_2\) // Sib. Math. J., 1999, vol. 40, pp. 905-917. 11. Li B. Real operator algebras. Institute of Mathematics. China: Acad. Sinica Beijing, 2002. 12. Sakai S. \(C^{\ast}\)-algebras and \(W^{\ast}\)-algebras. Springer, 1971. 13. Stormer E. Jordan algebras of type I // Acta. Math., 1966, vol. 115, pp. 165-184. 14. Topping D. M. Jordan algebras of self-adjoint operators // Mem. Am. Math. Soc., 1965, vol. 53. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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