2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170786An admissible observation operator is zero-class admissible if the norm of the output map tends to zero as the time tends to zero. Sufficient and necessary conditions for zero-class admissibility of observation operators are developed and a modified Weiss condition is studied. It is shown that the modified Weiss condition is in general necessary, but not sufficient for zero-class admissibility. For several important classes of C_0-semigroups it is proved that the modified Weiss condition is indeed equivalent to zero-class admissibility. The methods are illustrated by certain PDE examples.12 pagesFunctional AnalysisOptimization and Control93B07, 93B28 (Primary) 47D06, 47N70 (Secondary)text