2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128259We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to Hölder-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refine previous asymptotic trace formulas by Szegö and Widom and complement higher order asymptotic formulas for determinants of finite block Toeplitz matrices due to Böttcher and Silbermann.10 pagesFunctional AnalysisClassical Analysis and ODEsPrimary 47B35; Secondary 15A15, 47B10, 47L20, 47A68text