Notions of Subspace Hypercyclicity of Direct Sum of Operators

Abstract

Various notions of hypercyclicity have been studied over along period of time, however, complete characterization of this property has not been done. In fact, a lot of open questions remain unanswered with regard to subspace hypercyclicity. Most of these studies have been done in special cases of finite dimensional Banach spaces. It is therefore interesting to address these questions in general Banach spaces. In this research therefore we extend an investigation on subspace hypercyclicity by investigating different notions of the subspace hypercyclicity. We show that operators under direct sum satisfies various subspace-hypercyclicity criteria.