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Review

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

Department of Mathematics-Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
Mathematics 2020, 8(8), 1328; https://doi.org/10.3390/math8081328
Received: 23 July 2020 / Revised: 4 August 2020 / Accepted: 5 August 2020 / Published: 10 August 2020
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 fhg, 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. View Full-Text
Keywords: Hahn–Banach type theorems; Markov moment problem; sandwich theorem; finite-simplicial set; isotone convex operator; necessary and sufficient conditions Hahn–Banach type theorems; Markov moment problem; sandwich theorem; finite-simplicial set; isotone convex operator; necessary and sufficient conditions
MDPI and ACS Style

Olteanu, O. From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications. Mathematics 2020, 8, 1328. https://doi.org/10.3390/math8081328

AMA Style

Olteanu O. From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications. Mathematics. 2020; 8(8):1328. https://doi.org/10.3390/math8081328

Chicago/Turabian Style

Olteanu, Octav. 2020. "From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications" Mathematics 8, no. 8: 1328. https://doi.org/10.3390/math8081328

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