doi:10.1016/j.jmaa.2021.124984engAbadias, L.Bello, G.Yakubovich, D.Operator inequalities, functional models and ergodicityART-2021-123143We discuss when an operator T, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. The kernel need not be of Nevanlinna-Pick type. We define a defect operator D in our context and discuss the structure of the spectrum of T when D is of finite rank. As a second application, some consequences concerning the ergodic behavior of the operator T are derived.2021http://zaguan.unizar.es/record/9970110.1016/j.jmaa.2021.124984http://zaguan.unizar.es/record/99701oai:zaguan.unizar.es:99701info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MCYTS-DGI-FEDER/PID2019-105979GB-I00JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 498, 2 (2021), 124984 [39 pp]by-nc-ndhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccess