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arXiv · 1908.00291

Linear operators with infinite entropy

Will Brian·James P. Kelly
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Abstract

We examine the chaotic behavior of certain continuous linear operators on infinite-dimensional Banach spaces, and provide several equivalent characterizations of when these operators have infinite topological entropy. For example, it is shown that infinite topological entropy is equivalent to non-zero topological entropy for translation operators on weighted Lebesgue function spaces. In particular, finite non-zero entropy is impossible for this class of operators, which answers a question raised by Yin and Wei.

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Will Brian, James P. Kelly. 2019-08-01. Linear operators with infinite entropy. https://arxiv.org/abs/1908.00291

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