Cyclic behaviour of Volterra composition operators

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

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
251 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)535–562
Number of pages28
JournalProceedings of the London Mathematical Society
Volume103
Issue number3
DOIs
Publication statusPublished - Sep 2011

ASJC Scopus subject areas

  • Mathematics(all)

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