An Extension of Hypercyclicity for -Linear Operators

Juan Bès and J. Alberto Conejero

Abstract and Applied Analysis, 2014, vol. 2014, 1-11

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 -linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic -linear operators, for each . Indeed, the nonnormable spaces of entire functions and the countable product of lines support -linear operators with residual sets of hypercyclic vectors, for .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:609873

DOI: 10.1155/2014/609873

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