Journal of Operator Theory

Volume 65, Issue 1, Winter 2011 pp. 187-195.

Notes about weakly hypercyclic operators

Authors: Manuel de la Rosa
Author institution: Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.

Summary: The present article gives a brief discussion about operators which are weakly hypercyclic and answers the following three questions: (i) Must

$T \oplus T$ be weakly hypercyclic whenever

$T$ is? (ii) Is

$T^{n}$ weakly hypercyclic for every

$n \in \mathbb N$ whenever

$T$ is? (iii) Is

$\lambda T$ weakly hypercyclic for all

$|\lambda|=1$ whenever

$T$ is? Question (i) was explicitly posed by Chan and Sanders.

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