A continuous model for quasinilpotent operators

A classical result due to Foias and Pearcy establishes a discrete model

for every quasinilpotent operator acting on a separable, in nite-dimensional complex Hilbert space H. More precisely, given a quasinilpotent operator T on H, there exists a compact quasinilpotent operator K in H such that T is similar to a part of K ⊕K ⊕···⊕K ⊕··· acting on the direct sum of countably many copies of H. We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0-semigroups of quasinilpotent operators.