An Extension of Hypercyclicity for N-Linear Operators. (15th May 2014)

• Record Type: Journal Article
• Authors: Bès, Juan; Conejero, J. Alberto
• Other Names: Maestre Manuel Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-05-15
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/609873
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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 .