Various notions of subspace hypercyclic power operators and their direct sums in operator spaces

Subspace hypercyclic operators forms a very important class of operators in operator spaces.A lot of their properties 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 operator spaces.It is therefore interesting to address these questions in general operator spaces.In this research therefore we extend an investigation on subspace hypercyclicity by investigating different notions of the subspace hypercyclicity.In particular, we consider subspace hypercyclic operators, their powers and direct sums and show that operators under direct sum satisfies various subspace-hypercyclicity criteria and has a lot of interesting properties.