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arXiv · 1209.1458

A weighted bilateral shift with cyclic square is supercyclic

Stanislav Shkarin
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Abstract

It is shown that for a bounded weighted bilateral shift $T$ acting on $\ell_p(\Z)$ for $1\leq p\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient condition for cyclicity of a weighted bilateral shift is proved, which implies, in particular, that any compact weighted bilateral shift is cyclic.

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Stanislav Shkarin. 2012-09-07. A weighted bilateral shift with cyclic square is supercyclic. https://arxiv.org/abs/1209.1458

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