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2014 An Extension of Hypercyclicity for N -Linear Operators
Juan Bès, J. Alberto Conejero
Abstr. Appl. Anal. 2014(SI20): 1-11 (2014). DOI: 10.1155/2014/609873


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 .


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Juan Bès. J. Alberto Conejero. "An Extension of Hypercyclicity for N -Linear Operators." Abstr. Appl. Anal. 2014 (SI20) 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022716
MathSciNet: MR3212435
Digital Object Identifier: 10.1155/2014/609873

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI20 • 2014
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