Geodesic
Optimal reconstruction of a Banach function space from a cone of nonnegative functions
Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 142-156 
M. L. Goldman; P. P. Zabreiko. Optimal reconstruction of a Banach function space from a cone of nonnegative functions. Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 142-156. http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a7/
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     author = {M. L. Goldman and P. P. Zabreiko},
     title = {Optimal reconstruction of {a~Banach} function space from a~cone of nonnegative functions},
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     volume = {284},
     language = {ru},
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}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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