# Cyclic behaviour of Volterra composition operators

Stanislav Shkarin, A. Montes-Rodriguez, Alejandro Rodriguez-Martinez

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$, where$?$is a measurable self-map of [0, 1]. The cyclic behaviour of$V_\phi$is essentially determined by the behaviour of the inducing symbol$\phi\$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.