A duality result in locally convex cones. (English) Zbl 1503.46002

Dastouri, Amir; Ranjbari, Asghar

Positivity 26, No. 4, Paper No. 73, 13 p. (2022).

Summary: In this paper, we consider a locally convex cone \((\mathcal{P},\mathcal{V})\) and verify the dual of \((\operatorname{Conv}(\mathcal{P}),\overline{\mathcal{V}})\) the locally convex cone of the non-empty convex subsets of \(\mathcal{P}\). Under some semilattice conditions, we characterize the dual of \(\operatorname{Conv}(\underbrace{\dots}_{n\ \textrm{times}} (\operatorname{Conv}(\mathcal{P}))\).

MSC:

46A03	General theory of locally convex spaces
46A20	Duality theory for topological vector spaces

Keywords:

\(\bigvee\)-semilattice cone; locally convex cone; convex set

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