An Extension of Hypercyclicity for N-Linear Operators

Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N -linear operators that is inspired by difference equations. Under this new notion, every separable infinite d...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.860-870-982
Main Authors: Bès, Juan, Conejero, J. Alberto
Format: Article
Language:English
Subjects:
Cultivars
Forest & brush fires
Functional equations
Functions
Mathematical research
Nitrogen
Nonlinear theories
Vector spaces
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Summary:Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. 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 ≥ 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 .
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/609873