The binomial sequence spaces of nonabsolute type

Abstract

In this paper, we introduce the binomial sequence spaces b(0)(r,s) and b(c)(r,s) of nonabsolute type which include the spaces c(0) and c, respectively. Also, we prove that the spaces b(0)(r,s) and b(c)(r,s) are linearly isomorphic to the spaces c(0) and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their alpha-, beta-, and gamma-duals. Finally, we characterize some matrix classes related to those spaces.