Constant-norm scrambled sets for hypercyclic operators
type: Item
instance of: scholarly article
title: Constant-norm scrambled sets for hypercyclic operators
zbMATH Open document ID: 1233.47006
author: T. K. Subrahmonian Moothathu
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-01-04T00:00:00Z
review text: In this note, the author proves the following result on the scrambled set for a hypercyclic operator \(T\) on a separable Banach space \(X\): There is a linearly independent set \(S\) of hypercyclic vectors of \(T\) such that, for every \(r>0\) and for ever relatively open subset \(U\) of the sphere of radius \(r\) and center \(0\) in \(X\), the intersection \(S \cap U\) is nonempty, and every non-zero element of \(S-S\) is hypercyclic. The proof uses transfinite induction.
reviewed by: José Bonet
Mathematics Subject Classification ID: 47A16
zbMATH DE Number: 5994376
zbMATH Keywords: hypercyclic operators
zbMATH Keywords: Banach spaces
zbMATH Keywords: scrambled set
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.09.017
OpenAlex ID: W2029535988
cites work: Invariant manifolds of hypercyclic vectors for the real scalar case
cites work: Li-Yorke and distributionally chaotic operators
cites work: Invariant Manifolds of Hypercyclic Vectors
cites work: Limits of hypercyclic and supercyclic operators
cites work: Period Three Implies Chaos
cites work: Distributional chaos for backward shifts
cites work: Hypercyclic operators on non-locally convex spaces
DOI: 10.1016/J.JMAA.2011.09.017
description: scientific article; zbMATH DE number 5994376