Results 121 to 130 of about 1,158,171 (157)

Property (ω) and Hypercyclic Property for Operators

Wuhan University Journal of Natural Sciences
By means of the new spectrum defined with respect to the property of Consistence in Fredholm and Index (CFI) around an operator, we establish the necessary and sufficient conditions for a bounded linear opeator [see formula in PDF] defined on a Hilbert ...
Lei Dai, Jialu Yi
semanticscholar   +1 more source

Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators

Advances in Operator Theory
In this paper, we study property (UWE)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt ...
Simi Thomas, Thankarajan Prasad, Shery Fernandez   +2 more
semanticscholar   +1 more source

Hypercyclic and Chaotic Convolution Operators

Journal of the London Mathematical Society, 2000
Every convolution operator on a space of ultradifferentiable functions of Beurling or Roumieu type and on the corresponding space of ultradistributions is hypercyclic and chaotic (i.e., it is transitive and has a dense set of periodic points) when it is not a multiple of the identity.
openaire   +2 more sources

Faber-hypercyclic semigroups of linear operators

Filomat
In this research, the ?-hypercyclic and ?-transitive behavior are studied within the framework of linear strongly continuous semigroups. We give sufficient constraints on the spectrum of an operator to yield a ?-hypercyclic semigroup.
N. Karim, O. Benchiheb, M. Amouch
semanticscholar   +1 more source

A strictly weakly hypercyclic operator with a hypercyclic subspace

Journal of Operator Theory
An interesting topic of study for a hypercyclic operator T:X→X on a topological vector space X has been whether X has an infinite\hyp{}dimensional, closed subspace consisting entirely, except for the zero vector, of hypercyclic vectors of T. These subspaces are called hypercyclic subspaces. It has been known that there is an operator T:H→H on a Hilbert
Chan, Kit C., Madarasz, Zeno
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On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions

Mathematical Notes, 2023
Алсу Ильдаровна Рахимова, A. I. Rakhimova   +1 more
semanticscholar   +1 more source

Existence of hypercyclic operators

2011
In this chapter we obtain, among other things, the Ansari–Bernal theorem that every infinite-dimensional separable Banach space supports a hypercyclic operator. In contrast, some infinite-dimensional separable Banach spaces do not support any chaotic operator. We also discuss here the richness of the set of hypercyclic operators in two ways: it forms a
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
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Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators

Integral Equations and Operator Theory, 2007
We show that no power of any entire function is hypercyclic for Birkhoff’s translation operator on $$\mathcal{H}(\mathbb{C})$$ . On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane’s differentiation operator is a Gδ ...
R. M. Aron, J. A. Conejero, A. Peris, J. B. Seoane–Sepúlveda   +3 more
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Hypercyclic Conjugate Operators

Integral Equations and Operator Theory, 2006
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies \( \sup_{n} {\left| {w_{1} w_{2} \ldots w_{n} } \right|} = \infty \), the conjugate operator \( C_{B} :S \mapsto BSB^{*} \) is hypercyclic on the space S(H) of self-adjoint operators on H provided with the ...
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Pathological hypercyclic operators

Archiv der Mathematik, 2006
We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert space operator whose non-zero vectors are hypercyclic.
openaire   +1 more source