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arXiv · 1809.02549

${\mathcal F}$-Hypercyclic operators on Fr\' echet spaces

Marko Kostic
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Abstract

In this paper, we investigate ${\mathcal F}$-hypercyclicity of linear, not necessarily continuous, operators on Fr\' echet spaces. The notion of lower $(m_{n})$-hypercyclicity seems to be new and not considered elsewhere even for linear continuous operators acting on Fr\' echet spaces. We pay special attention to the study of $q$-frequent hypercyclicity, where $q\geq 1$ is an arbitrary real number. We present several new concepts and results for lower and upper densities in a separate section, providing also a great number of illustrative examples and open problems.

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Marko Kostic. 2018-09-07. ${\mathcal F}$-Hypercyclic operators on Fr\' echet spaces. https://arxiv.org/abs/1809.02549

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