A quasinilpotent operator is a bounded operator 
on a complex Banach space whose spectral
radius is zero. The spectral radius formula
expresses this condition as
 |
It does not require a power of 
to vanish. For example, a nilpotent
matrix is quasinilpotent: 
has 
. Quasinilpotence is a hypothesis in one formulation of
the hyperinvariant subspace problem.
