2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224794In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed that norm-unimodality is similar invariant and the spectra of norm-unimodal operator is referred to. As an application, in each nest algebra there exist distributional chaotic operators. Moreover, normal operators and compact operators with regard to norm-unimodality and Li-Yorke chaos are also be considered. Specially, a small compact perturbation of the unit operator could be distributionally chaotic.11 pagesFunctional AnalysisDynamical Systems47B37; 47B99; 54H20; 37B99text