Constrained Extension of Linear Operators, Approximation, and the Moment Problem
Octav Olteanu · Electronic Journal of Mathematics · 2021
Some Hahn-Banach-extension results for linear operators are reviewed.Several direct applications of these extension results to the existence of a solution for Markov moment problems are pointed out.A variant of the Mazur-Orlicz theorem in concrete spaces is also proved.Moreover, polynomial-approximation results on unbounded subsets and their applications to the existence and uniqueness of the solutions for the full Markov moment problem on R n and on R n + are reviewed.The multi-dimensional case is considered and the one-dimensional case follows as a consequence.Finally, the truncated moment problem is briefly discussed.