From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

Octav Olteanu
Additional contact information
Octav Olteanu: Department of Mathematics-Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania

Mathematics, 2020, vol. 8, issue 8, 1-16

Abstract: The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the following problems: (1) pointing out a previously published sandwich theorem of the type f ≤ h ≤ g , where f , − g are convex functionals and h is an affine functional, over a finite-simplicial set X , and proving a topological version for this result; (2) characterizing isotonicity of convex operators over arbitrary convex cones; giving a sharp direct proof for one of the generalizations of Hahn–Banach theorem applied to the isotonicity; (3) extending inequalities assumed to be valid on a small subset, to the entire positive cone of the domain space, via Krein–Milman or Carathéodory’s theorem. Thus, we point out some earlier, as well as new applications of the Hahn–Banach type theorems, emphasizing the topological versions of these applications.

Keywords: Hahn–Banach type theorems; Markov moment problem; sandwich theorem; finite-simplicial set; isotone convex operator; necessary and sufficient conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/8/1328/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/8/1328/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:8:p:1328-:d:396884

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().