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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.

Keywords:  Hypercyclic operators, weakly hypercyclic operators, direct sums of weakly hypercyclic operators, rotations of weakly hypercyclic operators

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