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arXiv · 1008.3267

Hypercyclic operators on topological vector spaces

Stanislav Shkarin
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Abstract

Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic operator on the locally convex direct sum of a sequence $\{X_n\}_{n\in\N}$ of Fréchet spaces if and only if each $X_n$ is separable and there are infinitely many $n\in\N$ for which $X_n$ is infinite dimensional. Moreover, we characterize inductive limits of sequences of separable Banach spaces which support a hypercyclic operator.

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Stanislav Shkarin. 2010-08-19. Hypercyclic operators on topological vector spaces. https://doi.org/10.1112/jlms%2Fjdr082

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