Spectral equality for $C_0$ semigroups
  In this paper, we give conditions for which the $C_0$ semigroups satisfies spectral equality for semiregular, essentially semiregular and semi-Fredholm spectrum. Also, we establish the spectral inclusion for B-Fredholm spectrum of a $C_0$ semigroups. 
A. Tajmouati, M. Amouch and M. R. F. Alhomidi Zakariya
math.SP