2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146278Following the classical approach of Pólya-Schur theory we initiate in this paper the study of linear operators acting on $\mathbb{R}[x]$ and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.15 pages, no figures, LaTeX2eClassical Analysis and ODEsFunctional Analysis12D15, 15A04 (Primary); 12D10 (Secondary)text