The binomial sequence spaces which include the spaces l(p) and l(infinity) and geometric properties

Abstract

In this work, we introduce the binomial sequence spaces b(p)(r,s) and b(infinity)(r,s) which include the spaces l(p) and l(infinity), in turn. Moreover, we show that the spaces b(p)(r,s) and b(infinity)(r,s) are BK-spaces and prove that these spaces are linearly isomorphic to the spaces l(p) and l(infinity), respectively. Furthermore, we speak of some inclusion relations and give the Schauder basis of the space b(p)(r,s). Lastly, we determine the alpha-,beta-, and gamma-duals of those spaces and give some geometric properties of the space b(p)(r,s).