The binomial sequence spaces of nonabsolute type

Abstract In this paper, we introduce the binomial sequence spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ of nonabsolute type which include the spaces c 0 $c_{0}$ and c, respectively. Also, we prove that the spaces b 0 r , s $b^{r,s}_{0}$ and b c r , s $b^{r,s}_{c}$ are linearly isomorphic to the spaces c 0 $c_{0}$ and c, in turn, and we investigate some inclusion relations. Moreover, we obtain the Schauder bases of those spaces and determine their α-, β-, and γ-duals. Finally, we characterize some matrix classes related to those spaces