On Some Binomial Sequence Space of Non-Absolute Type

Abstract

In this work, we introduce the binomial sequence spaces  and  which include the spaces  and , in turn. Moreover, we show that the spaces  and  are -spaces and prove that these spaces are linearly isomorphic to the spaces  and , respectively. Furthermore, we speak of some inclusion relations and give the Schauder basis of the space . Lastly, we determine the , and -duals of those spaces and give some geometric properties of the space .