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arXiv · 1209.1222

Universal elements for non-linear operators and their applications

Stanislav Shkarin
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Abstract

We prove that under certain topological conditions on the set of universal elements of a continuous map $T$ acting on a topological space $X$, that the direct sum $T\oplus M_g$ is universal, where $M_g$ is multiplication by a generating element of a compact topological group. We use this result to characterize $\R_+$-supercyclic operators and to show that whenever $T$ is a supercyclic operator and $z_1,...,z_n$ are pairwise different non-zero complex numbers, then the operator $z_1T\oplus {...}\oplus z_n T$ is cyclic. The latter answers affirmatively a question of Bayart and Matheron.

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Stanislav Shkarin. 2012-09-06. Universal elements for non-linear operators and their applications. https://arxiv.org/abs/1209.1222

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