Does the commutant of a quasinilpotent operator on a Banach space necessarily contain an operator with infinite spectrum? – mathoverflow.net

Let $X$ be an infinite-dimensional complex Banach space, and let $\mathcal{B}(X)$ denote the algebra of all bounded linear operators on $X$. For $T \in \mathcal{B}(X)$, write $\sigma(T)$ for its ...