2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224273The Fejer-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrix- and operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum's operator generalization of the classical Fejer-Riesz theorem.33 pages. To appear in the The Paul R. Halmos memorial volume in the series Operator Theory: Advances and Applications, published by Birhauser, edited by Sheldon Axler, Peter Rosenthal and Donald SarasonFunctional Analysis47A68 (Primary) 60G25, 47A56, 47B35, 42A05, 32A70, 30E99 (Secondary)text