Frequently recurrence properties and block families
R Cardeccia, S Muro - arXiv preprint arXiv:2204.13542, 2022 - arxiv.org
We study recurrence and the related $\mathscr P_\mathcal F $ property for linear operators
on Banach spaces. We show that for special families, called block families, hypercyclic …
on Banach spaces. We show that for special families, called block families, hypercyclic …
Shift operators and their classification
M Carvalho, UB Darji, P Varandas - arXiv preprint arXiv:2407.20890, 2024 - arxiv.org
We introduce a class of linear bounded invertible operators on Banach spaces, called shift
operators, which comprises weighted backward shifts and models finite products of …
operators, which comprises weighted backward shifts and models finite products of …
Linear dynamical systems
C Gilmore - arXiv preprint arXiv:2007.12647, 2020 - arxiv.org
This expository survey is dedicated to recent developments in the area of linear dynamics.
Topics include frequent hypercyclicity, $\mathcal {U} $-frequent hypercyclicity, reiterative …
Topics include frequent hypercyclicity, $\mathcal {U} $-frequent hypercyclicity, reiterative …
Frequently recurrent backward shifts
R Cardeccia, S Muro - arXiv preprint arXiv:2407.11799, 2024 - arxiv.org
We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet
sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent …
sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent …
Orthogonality of invariant measures for weighted shifts
S Grivaux, E Matheron, Q Menet - arXiv preprint arXiv:2312.13920, 2023 - arxiv.org
We introduce and study the notion of orthogonality for two operators in the context of
weighted backward shifts on $\ell_p (\mathbb {Z} _+) $, $1\leq p<\infty $. Two continuous …
weighted backward shifts on $\ell_p (\mathbb {Z} _+) $, $1\leq p<\infty $. Two continuous …
Common frequent hypercyclicity
S Charpentier, R Ernst, M Mestiri, A Mouze - Journal of Functional Analysis, 2022 - Elsevier
We provide with criteria for a family of sequences of operators to share a frequently universal
vector. These criteria are inspired by the classical Frequent Hypercyclicity Criterion and by a …
vector. These criteria are inspired by the classical Frequent Hypercyclicity Criterion and by a …
Two problems on weighted shifts in linear dynamics
F Bayart - Proceedings of the American Mathematical Society, 2021 - ams.org
Two problems on weighted shifts in linear dynamics Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 149, Number 12, December 2021, Pages …
AMERICAN MATHEMATICAL SOCIETY Volume 149, Number 12, December 2021, Pages …