نتایج جستجو برای: subspace frequently hypercyclic operators

تعداد نتایج: 293533  

Journal: :Journal of Mathematical Analysis and Applications 2021

In this short note, we answer a question of Martin and Sanders [Integr. Equ. Oper. Theory, 85 (2) (2016), 191-220] by showing the existence disjoint frequently hypercyclic operators which fail to be weakly mixing and, therefore, satisfy Disjoint Hypercyclicity Criterion. We also show that given an operator $T$ such $T \oplus T$ is hypercyclic, set $S$ $T, S$ are but Criterion SOT dense in algeb...

Journal: :Memoirs of the American Mathematical Society 2021

We solve a number of questions pertaining to the dynamics linear operators on Hilbert spaces, sometimes by using Baire category arguments and by constructing explicit examples. In particular, we prove following results. (i) A typical hypercyclic operator is not topologically mixing, has no eigenvalues admits non-trivial invariant measure, but densely distributionally chaotic. (ii) {upp...

2010
F. Bayart É. Matheron P. Moreau

We study the “smallness” of the set of non-hypercyclic vectors for some classical hypercyclic operators.

Journal: :Glasgow Mathematical Journal 2018

Journal: :Operators and Matrices 2018

Journal: :Proceedings of the American Mathematical Society 2022

We show that, under suitable conditions, an operator acting like a shift on some sequence space has frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts. also apply it every satisfying Frequent Hypercyclicity Criterion, recovering of Murillo and Peris.

2002
S. J. DILWORTH

Suppose that T is a bounded operator on a nonzero Banach space X . Given a vector x ∈ X , we say that x is hypercyclic for T if the orbit OrbTx = {T x}n is dense in X . Similarly, x is said to be weakly hypercyclic if OrbTx is weakly dense in X . A bounded operator is called hypercyclic or weakly hypercyclic if it has a hypercyclic or, respectively, a weakly hypercyclic vector. It is shown in [...

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