Geodesic
Construction of an optimal envelope for a~cone of nonnegative functions with monotonicity properties
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 43-61

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We study the problem of constructing a minimal quasi-Banach ideal space containing a given cone of nonnegative functions with monotonicity properties. The construction employs nondegenerate operators. We present general results on constructing optimal envelopes consistent with an order relation and obtain specifications of these constructions for various cones and various order relations. We also address the issue of order covering and order equivalence of cones. 
@article{TM_2016_293_a2,
     author = {E. G. Bakhtigareeva and M. L. Goldman},
     title = {Construction of an optimal envelope for a~cone of nonnegative functions with monotonicity properties},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {43--61},
     publisher = {mathdoc},
     volume = {293},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_293_a2/}
}
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E. G. Bakhtigareeva; M. L. Goldman. Construction of an optimal envelope for a~cone of nonnegative functions with monotonicity properties. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 43-61. http://geodesic.mathdoc.fr/item/TM_2016_293_a2/