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Functional realization of \(AW^*\)-algebras of type I. (English. Russian original) Zbl 0759.46052

Sib. Math. J. 32, No. 3, 416-424 (1991); translation from Sib. Mat. Zh. 32, No. 3(187), 78-88 (1991).
In the work of M. Ozawa [J. Math. Soc. Jap. 36, No. 4, 589-608 (1984; Zbl 0599.46083)] the invariants are described that characterize an \(AW^*\)-algebra of type I up to a \(*\)-isomorphism. These invariants are objects of Boolean valued inverse \(V^{(B)}\).
In the work being reviewed the analogous invariants are given that do not use the construction of \(V^{(B)}\). Moreover, the representations of \(AW^*\)-modules and \(AW^*\)-algebras of type I are given as spaces of continuous vector-valued functions and as algebras of strongly continuous operator-valued functions, respectively.

MSC:

46L10 General theory of von Neumann algebras
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46L05 General theory of \(C^*\)-algebras
03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

Citations:

Zbl 0599.46083
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References:

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