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On the structure of \(AJW\)-algebras of type \(I_2\). (English. Russian original) Zbl 0936.46040
Sib. Math. J. 40, No. 4, 764-774 (1999); translation from Sib. Mat. Zh. 40, No. 4, 905-917 (1999).
Author’s abstract: “A complete description for the structure of \(AJW\)-algebras of type \(I_2\) is given. In particular, some cardinal-valued invariants are indicated that characterize every algebra of this class up to isomorphism. We establish that each \(AJW\)-algebra of type \(I_2\) is constructed from abstract spin-factors by continuous or measurable ‘spreading’ and taking the direct sum. We find out conditions under which such a representation is unique. We use methods of Boolean-valued analysis”.

MSC:
46H70 Nonassociative topological algebras
46S20 Nonstandard functional analysis
17C65 Jordan structures on Banach spaces and algebras
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References:
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