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 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.
"Projections and isolated points of parts of the spectrum." Adv. Oper. Theory 3 (4) 868 - 880, Autumn 2018. https://doi.org/10.15352/aot.1804-1348