Document Type: Original Article
Universita di Palermo, Italy
In this paper, we relate the existence of certain projections, commuting with a bounded linear operator $T\in L(X)$ acting on Banach space $X$, with the generalized Kato decomposition GKD of $T$. We also relate the existence of these projections with some properties of the quasi-nilpotent part $H_0(T)$ and the analytic core $K(T)$. Further results are given for the isolated points of some parts of the spectrum.