What is the definition of a closed quasi-nilpotent operator in the norm sense?

137 Views Asked by At

How is defined a closed quasi-nilpotent operator in the norm sense ? I mean something like $\underset{n\rightarrow \infty }{\lim }\left\Vert A^{n}\right\Vert ^{\frac{1% }{n}}=0$ for a bounded quasi-nilpotent operator $A$.