Geodesic
Injectivity and nuclearity properties for real C*-algebras
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 755-765
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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$_\lambda$ ($0\lambda1$) are completely described. 
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A. A. Rakhimov; M. E. Nurillaev; Kh. Kh. Boltaev. Injectivity and nuclearity properties for real C*-algebras. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 755-765. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a7/

[1] Ayupov Sh. A., “Klassifikatsiya in'ektivnykh JW-faktorov”, Funkts. analiz i ego prilozh., 18:3 (1984), 67–68 | MR | Zbl

[2] Fon Neiman Dzh., “Obobschenie matematicheskogo apparata kvantovoi mekhaniki metodami abstraktnoi algebry. I”, Mat. sb., 1:4 (1936), 415–485

[3] Fon Neiman Dzh., Izbrannye trudy po funktsionalnomu analizu, v. I, II, Nauka, M., 1987

[4] Ayupov Sh. A., Rakhimov A. A., Usmanov Sh. M., Jordan, Real and Lie structures in operator algebras, Kluwer Academic Publishers, Dordrecht, 1997 | Zbl

[5] Ayupov Sh. A., Rakhimov A. A., Real W*-algebras, actions of groups and index theory for real factors, VDM Verlag Dr. Müller, Beau-Bassin, 2010

[6] Connes A., “Classification of injective facteurs”, Ann. Math., 104:1 (1976), 73–115 | DOI | MR | Zbl

[7] Dixmier J., Les algebres d'operateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969

[8] Grothendieck A., “Resume des results essentiels dans la theorie des produits tensoriels topologiques et des espaces nucleaires”, Ann. Inst. Fourier (Grenoble), 4 (1954), 73–112 | DOI

[9] Grothendieck A., “Produits tensoriels topologiques et des espaces nucléaires”, Séminaire N. Bourbaki, 69, 1954, 193–200

[10] Li B. R., Real operator algebras, World Scientific, River Edge, 2003 | Zbl

[11] Murray F., von Neumann J., “On rings of operators. I”, Ann. Math., 37 (1936), 116–229 | DOI | MR

[12] Rakhimov A. A., Nurillaev M. E., “On property of injectivity for real W*-algebras and JW-algebras”, Positivity, 22 (2018), 1345–1354 | DOI | MR | Zbl

[13] Sakai S., C*-algebras and W*-algebras, Springer, Berlin, 1971 | Zbl

[14] Stacey P. J., “Real structure in unital separable simple C*-algebras with tracial rank zero and with a unique tracial state”, New York J. Math., 12 (2006), 269–273 | MR | Zbl

[15] Stormer E., “Real structure in the hyperfinite factor”, Duke Math. J., 47:1 (1980), 145–153 | DOI | MR | Zbl

[16] Takesaki M., Theory of operator algebras, v. I, II, III, Springer, Berlin, 1979 | Zbl