Description of Real $AW^*$-Factors of Type I

Sh. A. Ayupov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: 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.

UDC: 517.98

Received: 07.08.2003

DOI: 10.4213/mzm108

 English version: Mathematical Notes, 2004, 76:3, 323–328

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