Abstract

A bounded linear operator T defined on a Hilbert space H is said to be supercyclic if there exists a vector x in H such that the set {λTⁿx : n in N, λ in 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.

Authors