This article is cited in 2 papers

Brief communications

Real $AW^*$-Algebras of Type I

Sh. A. Ayupov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: Let $R$ be a real $AW^*$-algebra, and suppose that its complexification $M=R+iR$ is also a (complex) $AW^*$-algebra. We prove that $R$ is of type $\mathrm{I}$ if and only if so is $M$.

Keywords: real $C^*$-algebra, real $W^*$-algebra, real $AW^*$-algebra, complexification, type $\mathrm{I}$ algebra.

UDC: 517.98

Received: 18.04.2003

DOI: 10.4213/faa128

 English version: Functional Analysis and Its Applications, 2004, 38:4, 302–304

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