2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66599In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.5 pagesFunctional Analysis47B20, 47B37text