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Description of Real AW*-Factors of Type I

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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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  1. Institute of Mathematics, Uzbek Academy of Sciences, Tashkent, Russia

    Sh. A. Ayupov

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  1. Sh. A. Ayupov
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Ayupov, S.A. Description of Real AW*-Factors of Type I. Mathematical Notes 76, 323–328 (2004). https://doi.org/10.1023/B:MATN.0000043459.27757.bc

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  • DOI: https://doi.org/10.1023/B:MATN.0000043459.27757.bc

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