In [13], Ptak and Vrbova proved that if T is a bounded normal operator T on a complex Hilbert space H, then the ranges of the spectral projections can be represented in the form $$ varepsilon(F)H = igcap_{lambda otinF} (T - lambda I) H for all closed subsets F of C, $$ where $varepsilon$ denotes the spectral measure associated with T.