# On Hahn-Banach theorem and some of its applications

@article{Olteanu2022OnHT, title={On Hahn-Banach theorem and some of its applications}, author={Octav Olteanu}, journal={Open Mathematics}, year={2022}, volume={20}, pages={366 - 390} }

Abstract First, this work provides an overview of some of the Hahn-Banach type theorems. Of note, some of these extension results for linear operators found recent applications to isotonicity of convex operators on a convex cone. Next, the work investigates applications of the Krein-Milman theorem to representation theory and elements of Choquet theory. A sandwich theorem of intercalating an affine function h h between f f and g , g, where f f\hspace{.25em} and – g \mbox{--}g are convex, f ≤ g…

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## References

SHOWING 1-10 OF 12 REFERENCES

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

- Mathematics
- 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…

On Markov Moment Problem and Related Results

- MathematicsSymmetry
- 2021

New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.

Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

- Mathematics
- 2020

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under…

On truncated and full classical Markov moment problems

- Mathematics
- 2021

Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤…

From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory

- MathematicsRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
- 2020

The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya…

On the Momentum Problem for Distribution Functions in More Than One Dimension. II

- Mathematics
- 1935

is likewise non-negative. A. Wintner has subsequently suggested that it should be possible to extend this result by requiring that the distribution function solving the problem have a spectrum…

Convex Functions and Their Applications: A Contemporary Approach

- Mathematics
- 2005

This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some o…

Topological Vector Spaces

- Mathematics, Physics
- 2003

These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.