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arXiv · 2605.07563

On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces

Nacib G. Albuquerque·Thiago R. Alves·Geraldo Botelho·Vinícius V. Fávaro
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Abstract

Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof technique we develop also allows us to prove that $B$ admits a hypercyclic subspace free of $\mathscr{U}$-frequently hypercyclic vectors, and to solve a question posed by B\`es and Menet in 2015 on the existence of common $\mathscr{U}$-frequently hypercyclic subspaces.

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Nacib G. Albuquerque, Thiago R. Alves, Geraldo Botelho, Vinícius V. Fávaro. 2026-05-08. On hypercyclic spaces and (common) $\mathscr{U}$-frequently hypercyclic spaces. https://arxiv.org/abs/2605.07563

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