\mathcal F-Hypercyclic operators on Fr' echet spaces

2018/09/07 by Kostic, Marko
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1809.02549

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≥ 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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