Normality in real AW*-algebras
- Authors: Chepukhalin S.A.1,2, Rakhimov A.A.3
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Affiliations:
- Tashkent University of Information Technology
- Plekhanov Russian State University of Economics
- National University of Uzbekistan named after Mirzo Ulugbek
- Issue: Vol 243 (2025)
- Pages: 78-80
- Section: Articles
- URL: https://ogarev-online.ru/2782-4438/article/view/312584
- DOI: https://doi.org/10.36535/2782-4438-2025-243-78-80
- ID: 312584
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Abstract
This paper is devoted to the study of the concept of normality in real AW*-algebras. The authors examine whether normality is preserved when passing from a complex AW*-algebra to its real part and prove that all real AW*-factors are normal. Conditions are established under which a real AW*-algebra is normal, in particular, when its center is locally $\sigma$-finite. The obtained results serve as real analogs of known theorems on normality in AW*-algebras and contribute to the development of operator algebra theory in the real setting.
Keywords
About the authors
Sergey Anatol'evich Chepukhalin
Tashkent University of Information Technology; Plekhanov Russian State University of Economics
Abdugafur Abdumadjidovich Rakhimov
National University of Uzbekistan named after Mirzo UlugbekDoctor of physico-mathematical sciences, Professor
References
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- Rakhimov A. A., Nurillaev M. E., Boltaev K. K., “Injectivity and nuclearity properties for real C-algebras”, J. Math. Sci., 278:3 (2024), 520–529
- Saito K., Wright J. D. M., “All AW-factors are normal”, J. London Math. Soc. (2)., 44 (1991), 143–154
- Wright J. D. M., “Normal AW-algebras”, Proc. Roy. Soc. Edinburgh A., 85 (1980), 137–141
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