## Abstract and Applied Analysis

### An Extension of Hypercyclicity for $N$-Linear Operators

#### 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 $N\ge 2$. Indeed, the nonnormable spaces of entire functions and the countable product of lines support $N$-linear operators with residual sets of hypercyclic vectors, for $N=2$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 609873, 11 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412278776

Digital Object Identifier
doi:10.1155/2014/609873

Mathematical Reviews number (MathSciNet)
MR3212435

Zentralblatt MATH identifier
07022716

#### Citation

Bès, Juan; Conejero, J. Alberto. An Extension of Hypercyclicity for $N$ -Linear Operators. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 609873, 11 pages. doi:10.1155/2014/609873. https://projecteuclid.org/euclid.aaa/1412278776

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