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Operator-valued measurable functions. (English) Zbl 1328.46045

Summary: Let \(\Omega\) be a measurable space and \(\mathcal{M}\) be a \(\sigma\)-finite von Neumann algebra which is also a second dual space. On the set of functions from \(\Omega\) into \(\mathcal{M}\), it is supposed to give a criterion to illustrate \(\tau\)-measurability where \(\tau\) runs over some well-known locally convex topologies on \(\mathcal{M}\) which are stronger than the weak operator topology and weaker than the Arens-Mackey topology.

MSC:

46L10 General theory of von Neumann algebras
47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones)
46G10 Vector-valued measures and integration
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Full Text: Euclid