منابع مشابه
Difference sets and frequently hypercyclic weighted shifts
We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on l(Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently...
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In the following text for arbitrary $X$ with at least two elements, nonempty countable set $Gamma$ we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map. We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney, exact Dev...
متن کاملcounterexamples in chaotic generalized shifts
in the following text for arbitrary $x$ with at least two elements, nonempty countable set $gamma$ we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map. we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney, exact dev...
متن کاملHypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup
Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.
متن کاملOn Polynomially Bounded Weighted Shifts
(1) ‖p(T )‖ ≤M sup{|p(ζ)| : |ζ| = 1} ∀ polynomial p, and to be power bounded (notation T ∈ (PW)) if (1) holds for every polynomial of the special form p(ζ) = ζ where n is a positive integer. If T ∈ (PB) [resp., T ∈ (PW)], then there is a smallest number M which satisfies (1) [resp., (1) restricted]. This number will be called the polynomial bound of T [resp., the power bound of T ] and denoted ...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2000
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-139-1-47-68