Cyclic properties of Volterra operator

Fernando León-Saavedra and Antonio Piqueras-Lerena

Vol. 211 (2003), No. 1, 157–162

DOI: 10.2140/pjm.2003.211.157

Abstract

A bounded linear operator T defined on a Hilbert space H is said to be supercyclic if there exists a vector x ∈ H such that the set {λTⁿx : n ∈ ℕ, λ ∈ ℂ} is dense in H. In the present work, two open questions posed by N. H. Salas and J. Zemánek respectively, are solved. Namely, we will exhibit that the classical Volterra operator V and the identity plus Volterra operator I + V are not supercyclic.

Milestones

Received: 12 August 2002

Published: 1 September 2003