On the Power Set of Quasinilpotent Operators in Banach Spaces

C. L. Hu, Y. Q. Ji, D. H. Liang

For a quasinilpotent operator $T$ on a Banach space $X$, Douglas and Yang defined $k_x=\underset{\lambda \to 0}{\mathrm{limsup}}\frac{\ln \Vert (\lambda -T{)}^{-1}x\Vert }{\ln \Vert (\lambda -T{)}^{-1}\Vert }$ for each non-z…