An Extension of Hypercyclicity for N‐Linear Operators

Juan Bès and J. Alberto Conejero

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/609873

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:609873

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