  In this paper, we show that for a bounded linear operator $T$, the
corresponding generalized Kato decomposition spectrum $\sigma_{gK}(T)$
satisfies the equality $\sigma_{gD}(T)=\sigma_{gK}(T)\cup (S(T)\cup S(T^*))$
where $\sigma_{gD} (T ) $ is the generalized Drazin spectrum of $T$ and $S(T )$
(resp., $S(T^*)$ is the set where T (resp., $T^*$) fails to have SVEP. As
application, we give sufficient conditions which assure that the generalized
Kato decomposition spectrum of an upper triangular operator matrices is the
union of its diagonal entries spectra. Moreover, some applications are given.
