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Optimal domains for \(L^{0}\)-valued operators via stochastic measures. (English) Zbl 1148.46026
Let \(T:E\to L^0([0,1])\) be a linear operator, where \(E\) is a function space and \(L^0([0,1])\) the space of measurable functions with the topology of convergence in measure. The authors study conditions on \(T\) and \(E\) that allow them to extend the operator \(T\) to domains larger than \(E\) and in this case to study the properties of such domains.

MSC:
46G10 Vector-valued measures and integration
47B38 Linear operators on function spaces (general)
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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