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Optimal reconstruction of a Banach function space from a cone of nonnegative functions. (English. Russian original) Zbl 1318.46015

Proc. Steklov Inst. Math. 284, 133-147 (2014); translation from Tr. Mat. Inst. Steklova 284, 142-156 (2014).
Summary: We study the problem of constructing a minimal Banach function space containing a given cone of nonnegative measurable functions. For the associate function norm of the norm of an optimal space, we obtain general formulas and specify them in the case of a cone defined by an integral representation. We also consider the similar problem of constructing an optimal rearrangement invariant space and compare the descriptions obtained.

MSC:

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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