A. A. Rakhimov, M. E. Nurillaev, Kh. Kh. Boltaev, “Injectivity and nuclearity properties for real C*-algebras”, CMFD, 2021, Volume 67, Issue 4,Pages <nobr>755

Injectivity and nuclearity properties for real C*-algebras

A. A. Rakhimov^ab, M. E. Nurillaev^c, Kh. Kh. Boltaev^c

^a National University of Uzbekistan named after M. Ulugbek, Tashkent, Uzbekistan
^b Karadeniz Teknik Üniversitesi, Trabzon, Turkey
^c Tashkent State Pedagogical University named after Nizami, Tashkent, Uzbekistan

Abstract: In this paper, we study injective and nuclear real W$^*$- and C$^*$-algebras. The connection of these concepts with similar concepts of enveloping W$^*$- and C$^*$-algebras is considered. The equivalence of the concepts of injectivity and nuclearity for real C$^*$-algebras is shown. As a consequence, nuclear real factors of types II$_1,$ II$_\infty,$ III$_1,$ III$_0,$ and III$_\lambda$ ($0<\lambda<1$) are completely described.

UDC: 517.98

DOI: 10.22363/2413-3639-2021-67-4-755-765