PreprintarXiv licencearXiv
On hypercyclic and (common) upper frequently hypercyclic subspaces
Abstract
Let B be a unilateral weighted backward shift on ℓp, 1 ≤ p < ∞, that admits a 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 𝒰-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common 𝒰-frequently hypercyclic subspaces.
Related
- Existence of hypercyclic algebras in Fréchet algebras
- Hypercyclic Bergman-Toeplitz operators with some harmonic symbols
- Weighted orbits of hypercyclic vectors on F-spaces
- Hypercyclic and topologically transitive semigroups of composition operators (revised and extended version)
- Subspaces of L1 spanned by the even and odd levels of the Haar system
BibTeX
@misc{albuquerque2026hypercyclic,
title = {{On hypercyclic and (common) upper frequently hypercyclic subspaces}},
author = {Nacib G. Albuquerque and Thiago R. Alves and Geraldo Botelho and Vinícius V. Fávaro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.07563},
eprint = {2605.07563},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.07563},
}
RIS
TY - UNPB
TI - On hypercyclic and (common) upper frequently hypercyclic subspaces
AU - Nacib G. Albuquerque
AU - Thiago R. Alves
AU - Geraldo Botelho
AU - Vinícius V. Fávaro
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2605.07563
UR - https://arxiv.org/abs/2605.07563
AB - Let B be a unilateral weighted backward shift on ℓ_p, 1 ≤ p < ∞, that admits a 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 𝒰-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common 𝒰-frequently hypercyclic subspaces.
ER -