Abstract.

In this article, the sequence spaces c0(N t ) and c(N t ) are introduced as the domain of N¨orlund mean N t in the spaces c0 and c of null and convergent sequences which are isomorphic to the spaces c0 and c, respectively, and some inclusion relations are given. Additionally, Schauder basis for the spaces c0(N t ) and c(N t ) are constructed and their alpha-, beta- and gamma-duals are computed. Finally, the classes (c(N t ) : `∞), (c(N t ) : c) and (c(N t ) : c0) of matrix transformations are characterized.

Keywords:

matrix domain, spaces of convergent and null sequences, N¨orlund matrix, alpha-, beta- and gamma-duals and matrix transformations.