Non-supercyclicity of Volterra convolution and related operators

Research output: Contribution to journalArticlepeer-review


We show that if V-alpha (alpha > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L-2(0, 1) which commutes with V, then TV alpha is not supercyclic on L-2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used by Gallardo-Gutierrez and Montes-Rodriguez to show that V is not supercyclic.

Original languageEnglish
Pages (from-to)585-589
Number of pages5
JournalIntegral Equations and Operator Theory
Issue number4
Publication statusPublished - Dec 2008


  • Supercyclic
  • Volterra convolution
  • fractional integration operator

Cite this