Geodesic
Description of Real $AW^*$-Factors of Type~I
Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 344-349

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In the paper, real $AW^*$-algebras are considered, i.e., real $C^*$-algebras which are Baer *-rings. It is proved that every real $AW^*$-factor of type I (i.e., having a minimal projection) is isometrically *-isomorphic to the algebra $B(H)$ of all bounded linear operators on a real or quaternionic Hilbert space $H$ and, in particular, is a real $W^*$-factor. In the case of complex $AW^*$-algebras, a similar result was proved by Kaplansky. 
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     author = {Sh. A. Ayupov},
     title = {Description of {Real} $AW^*${-Factors} of {Type~I}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {344--349},
     publisher = {mathdoc},
     volume = {76},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a3/}
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Sh. A. Ayupov. Description of Real $AW^*$-Factors of Type~I. Matematičeskie zametki, Tome 76 (2004) no. 3, pp. 344-349. http://geodesic.mathdoc.fr/item/MZM_2004_76_3_a3/