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arXiv · 2206.01508

Supercyclic vectors of operators on normed linear spaces

Mohammad Ansari
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Abstract

We give an affirmative answer to a question asked by Faghih-Ahmadi and Hedayatian regarding supercyclic vectors. We show that if $\mathcal X$ is an infinite-dimensional normed linear space and $T$ is a supercyclic operator on $\mathcal X$, then for any supercyclic vector $x$ for $T$, there exists a strictly increasing sequence $(n_k)_k$ of positive integers such that the closed linear span of the set $\{T^{n_k}x: k\ge 1\}$ is not the whole $\mathcal X$.

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Mohammad Ansari. 2022-06-03. Supercyclic vectors of operators on normed linear spaces. https://arxiv.org/abs/2206.01508

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