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 $k_x=\underset{\hat{I}»\to 0}{\mathrm{limsup}}\frac{\ln \Vert (\hat{I}»-T{)}^{-1}x\Vert }{\ln \Vert (\hat{I}»-T{)}^{-1}\Vert }$ for each no…