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Eurasian Math. J., 2019, Volume 10, Number 1, Pages 59–79 (Mi emj323)  

Hahn–Banach type theorems on functional separation for convex ordered normed cones

F. S. Stonyakin

Department of algebra and functional analysis, Crimea Federal University, 4 V. Vernadsky Ave, Simferopol

Abstract: We consider a special class of convex ordered normed cones CONC. For such structures we obtain Hahn–Banach type theorems on functional separation for points. On the base of a Hahn–Banach type theorem on functional separation for points we prove a sublinear version of the Rädström embedding theorem for the class CONC. Some analogues of Hahn–Banach separation theorem for some type of sets in CONC are obtained.

Keywords and phrases: abstract convex cone, Hahn–Banach separation theorem, strict convex normed cone, convex ordered normed cone, sublinear injective isometric embedding, Rädström embedding theorem.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation MK-176.2017.1
This work was partially supported by the grant of the President of Russian Federation for young candidates of sciences, project no. MK-176.2017.1.


DOI: https://doi.org/10.32523/2077-9879-2019-10-1-59-79

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MSC: 46A22, 46A20, 46B10
Received: 20.02.2017
Revised: 06.09.2018
Language:

Citation: F. S. Stonyakin, “Hahn–Banach type theorems on functional separation for convex ordered normed cones”, Eurasian Math. J., 10:1 (2019), 59–79

Citation in format AMSBIB
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\by F.~S.~Stonyakin
\paper Hahn--Banach type theorems on functional separation for convex ordered normed cones
\jour Eurasian Math. J.
\yr 2019
\vol 10
\issue 1
\pages 59--79
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