Operators commuting with the Volterra operator are not weakly supercyclic

Abstract

We prove that any bounded linear operator on $L_p[0,1]$ for $1\le p<\infty$, commuting with the Volterra operator $V$, is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with $V$.

Submitted to LMS

References in corpus (1)

• Weak cluster points of a sequence and coverings by cylinders