2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145029We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain special factorizations that involve thematic matrix functions.Functional AnalysisClassical Analysis and ODEsComplex VariablesSpectral Theory30E10; 47B35text