On the M-hypercyclicity of cosine function on Banach spaces

Abdelaziz Tajmouati; Abdeslam El Bakkali; Ahmed Toukmati

doi:10.5269/bspm.v38i3.38137

On the M-hypercyclicity of cosine function on Banach spaces

Abdelaziz Tajmouati Sidi Mohamed Ben Abdellah University Faculty of Sciences Dhar El Mahraz Laboratory of Mathematical Analysis and Applications http://orcid.org/0000-0003-1572-1241
Abdeslam El Bakkali Chouaib Doukkali University Faculty of Sciences El Jadida
Ahmed Toukmati Sidi Mohamed Ben Abdellah University Faculty of Sciences Dhar El Mahraz Laboratory of Mathematical Analysis and Applications

DOI: https://doi.org/10.5269/bspm.v38i3.38137

Keywords: Cosine function, Hypercyclicity, Topologically transitive, M-hypercyclicity, M-transitive

Abstract

In this paper we introduce and study the M-hypercyclicity of strongly continuous cosine function on separable complex Banach space, and we give the criteria for cosine function to be M-hypercyclic. We also prove that every separable infinite dimensional complex Banach space admits a uniformly continuous cosine function.