Results 1 to 10 of about 2,965 (120)
Disjoint hypercyclicity, Sidon sets and weakly mixing operators [PDF]
Ergodic Theory and Dynamical Systems, 2022 We prove that a finite set of natural numbers J satisfies that $J\cup \{0\}$ is not Sidon if and only if for any operator T, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that T is weakly mixing. As an application we show the existence of a
Rodrigo Cardeccia
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Multiple recurrence and hypercyclicity [PDF]
Mathematica Scandinavica, 2021 We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where $\mathcal F$ is the family of subsets of the natural numbers containing arbitrarily long arithmetic progressions. We prove several properties of
Rodrigo Cardeccia, Santiago Muro
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Commutant hypercyclicity of Hilbert space operators
Filomat, 2023 An operator T on a Hilbert space H is commutant hypercyclic if there is a vector x in H such that the set {Sx : TS = ST} is dense in H. We prove that operators on finite dimensional Hilbert space, a rich class of weighted shift operators, isometries ...
Karim Hedayatian +1 more
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Non‐Diskcyclicity of Bounded Composition Operators on the Little Bloch Space and the Besov Space
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, we show that there are no diskcyclic composition operators on the little Bloch space ℬ0 and the Besov spaces Bp.
Hang Zhou +2 more
wiley +1 more source
On the Recurrent C0‐Semigroups, Their Existence, and Some Criteria
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, recurrent C0‐semigroups are introduced and investigated. It is proved that, despite hypercyclic C0‐semigroups, recurrent C0‐semigroups can be found on finite‐dimensional Banach spaces. Some criteria are stated for recurrence, which is based on open sets, neighborhoods of zero, and special eigenvectors.
Mansooreh Moosapoor, Tuncer Acar
wiley +1 more source
Topological Transitivity of Shift Similar Operators on Nonseparable Hilbert Spaces
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this paper, we investigate topological transitivity of operators on nonseparable Hilbert spaces which are similar to backward weighted shifts. In particular, we show that abstract differential operators and dual operators to operators of multiplication in graded Hilbert spaces are similar to backward weighted shift operators.
Andriy Zagorodnyuk +2 more
wiley +1 more source
Journal of Mathematical Sciences, 2022 A continuous linear operator on a Fréchet space X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-
F. León-Saavedra, M. D. L. de la Rosa
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Chaos and frequent hypercyclicity for composition operators [PDF]
Proceedings of the Edinburgh Mathematical Society, 2020 The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Ruzsa in 2015 that for backward weighted shifts on $\ell _p(\mathbb {Z})$, the ...
U. Darji, B. Pires
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Cyclicity, hypercyclicity and randomness in self-similar groups [PDF]
Monatshefte für Mathematik (Print)We introduce the concept of cyclicity and hypercyclicity in self-similar groups as an analogue of cyclic and hypercyclic vectors for an operator on a Banach space.
Jorge Fariña-Asategui
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Hereditarily frequently hypercyclic operators and disjoint frequent hypercyclicity [PDF]
Ergodic Theory and Dynamical SystemsWe introduce and study the notion of hereditary frequent hypercyclicity, which is a reinforcement of the well-known concept of frequent hypercyclicity.
F. Bayart +3 more
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