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 where are convex functionals and is an affine functional, over a finite-simplicial set 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.

中文翻译：

---

从Hahn–Banach型定理到Markov矩问题，三明治定理和进一步的应用

本文的目的是回顾两个马尔可夫矩问题的已知解，这些解可以表述为Hahn–Banach扩展定理，以便强调它们与以下问题的关系：（1）指出先前发布的夹心定理在有限单纯性集合上凸函数且是仿射函数的类型，并为此结果证明是拓扑形式；（2）刻画任意凸锥上凸算子的等渗性；为应用于等张性的Hahn–Banach定理的一种概括提供了清晰的直接证明；（3）通过Krein-Milman或Carathéodory定理，将假定对一个小子集有效的不等式扩展到域空间的整个正锥。因此，我们较早地指出，