An Analogue of the Hahn-Banach Theorem for Functionals on Abstract Convex Cones


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Authors

  • Fedor Sergeevich Stonyakin

Keywords:

abstract convex cone, cancellation law, convex functional, Hahn-Banach theorem, convex normed cone, Lemma on a support functional, strict convex normed cone, sublinear injective isometric embedding

Abstract

We prove an analogue of the Hahn-Banach theorem on the extension of a linear functional with a convex estimate for each abstract convex cone with the cancellation law. Also we consider the special class of the so-called strict convex normed cones (SCNC). For such structures we obtain an appropriate analogue of the Hahn-Banach separation theorem. On the base of this result we prove that each (SCNC) is sublinearly, injectively and isometrically embedded in some Banach space.

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Published

2016-09-30

How to Cite

Stonyakin, F. S. (2016). An Analogue of the Hahn-Banach Theorem for Functionals on Abstract Convex Cones. Eurasian Mathematical Journal, 7(3), 89–99. Retrieved from https://emj.enu.kz/index.php/main/article/view/644

Issue

Vol. 7 No. 3 (2016)

Section

Articles