Abstract:
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.
Citation:
E. G. Bakhtigareeva, M. L. Goldman, “Construction of an optimal envelope for a cone of nonnegative functions with monotonicity properties”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 43–61; Proc. Steklov Inst. Math., 293 (2016), 37–55
\Bibitem{BakGol16}
\by E.~G.~Bakhtigareeva, M.~L.~Goldman
\paper Construction of an optimal envelope for a~cone of nonnegative functions with monotonicity properties
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 43--61
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968516020035}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 293
\pages 37--55
\crossref{https://doi.org/10.1134/S0081543816040039}
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https://www.mathnet.ru/eng/tm3703
https://doi.org/10.1134/S0371968516020035
https://www.mathnet.ru/eng/tm/v293/p43
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