Epsilon-hypercyclic operators

Badea, Catalin; Grivaux, Sophie; Müller, Vladimir

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1017/S0143385709000765

Permalink :

http://hdl.handle.net/20.500.12210/122237

Title :

Epsilon-hypercyclic operators

Author(s) :

Badea, Catalin [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Grivaux, Sophie [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Müller, Vladimir [Auteur]

Journal title :

Ergodic Theory and Dynamical Systems

Pages :

1597-1606

Publisher :

Cambridge University Press (CUP)

Publication date :

2010-12

ISSN :

0143-3857

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Abstract Let X be a separable infinite-dimensional Banach space, and T a bounded linear operator on X ; T is hypercyclic if there is a vector x in X with dense orbit under the action of T . For a fixed ε∈(0,1), we say that ...
Show more >Abstract Let X be a separable infinite-dimensional Banach space, and T a bounded linear operator on X ; T is hypercyclic if there is a vector x in X with dense orbit under the action of T . For a fixed ε∈(0,1), we say that T is ε-hypercyclic if there exists a vector x in X such that for every non-zero vector y ∈ X there exists an integer n with $\|T^nx-y\|\leq \varepsilon \|y\|$ . The main result of this paper is a construction of a bounded linear operator T on the Banach space ℓ 1 which is ε-hypercyclic without being hypercyclic. This answers a question from V. Müller [Three problems, Mini-Workshop: Hypercyclicity and linear chaos, organized by T. Bermudez, G. Godefroy, K.-G. Grosse-Erdmann and A. Peris. Oberwolfach Rep. 3 (2006), 2227–2276].Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T15:33:41Z

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