Weighted composition operators as Daugavet centers

We investigate the norm identity ‖ u C φ + T ‖ = ‖ u ‖ ∞ + ‖ T ‖ for classes of operators on C ( S ) , where S is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy this equation for every weakly compact operator T : C ( S ) → C ( S ) . We also give a characterization of such weighted composition operator acting on the disk algebra A ( D ) .