An extension of hypercyclicity for \(N\)-linear operators
type: Item
instance of: scholarly article
title: An extension of hypercyclicity for \(N\)-linear operators
zbMATH Open document ID: 1473.47001
DOI: 10.1155/2014/609873
author: J. Bès
author: José Alberto Conejero
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators [\textit{K.-G. Grosse-Erdmann} and \textit{S. G. Kim}, J. Math. Anal. Appl. 399, No. 2, 701--708 (2013; Zbl 1272.47009)]. We propose an alternative notion of orbit for \(N\)-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic \(N\)-linear operators, for each \(N \geq 2\). Indeed, the nonnormable spaces of entire functions and the countable product of lines support \(N\)-linear operators with residual sets of hypercyclic vectors, for \(N = 2\).
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 7022716
zbMATH Keywords: bihypercyclicity
zbMATH Keywords: existence of dense orbits
zbMATH Keywords: \(N\)-linear operators
zbMATH Keywords: supercyclic \(N\)-linear operators
Wikidata QID: Q59039924
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/609873
OpenAlex ID: W1998618871
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description: scientific article; zbMATH DE number 7022716