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Borel maps in real reduction theory. (English) Zbl 1105.46041

Summary: In B.–R.Li [Sci.China, Ser. A, 41, 574–581 (1998; Zbl 0968.46048)], we gave a real reduction theory. It is the real analogue of J. von Neumann’s (complex) reduction theory. In [Pac.J.Math.15, 1153–1164 (1965; Zbl 0135.36102)], E. G.Effros gave a natural explanation for (complex) reduction theory by Borel maps. In the present note, we also use Borel maps to give an explanation for real measurable fields of Hilbert spaces, von Neumann algebras, etc.

MSC:

46L10 General theory of von Neumann algebras
46L45 Decomposition theory for \(C^*\)-algebras
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