Unilateral weighted shifts on $\ell^2$

Konstantinos A. Beros; Paul B. Larson

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arXiv · 1904.03782

Unilateral weighted shifts on $\ell^2$

Konstantinos A. Beros·Paul B. Larson

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Abstract

Given a unilateral shift $B_w$ (determined by a bounded sequence $w$), a sequence $x \in \ell^2$ is "hypercyclic" for $w$ iff the forward iterates of $x$ under $B_w$ are dense in $\ell^2$. We show that it is possible to make the set of $x \in \ell^2$ which are simultaneously hypercyclic for all $w$ in a fixed $W \subseteq \ell^\infty$ arbitrarily complicated by choosing $W$ appropriately.

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BibTeX RIS

Konstantinos A. Beros, Paul B. Larson. 2020-06-08. Unilateral weighted shifts on $\ell^2$. https://arxiv.org/abs/1904.03782

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