The Hahn Sequence Space Defined by the Cesáro Mean

Abstract

The $BK$-space of all sequences is given as $x=(x_k)$ such that ${\Sigma }_{k=1}^{\infty }k|x_k-x_{k+1}|$ converges and $x_k$ is a null sequence which is called the Hahn sequence space and is denoted by $h$. Hahn (1922) defined the $h$ space and gave some general properties. G. Goes and S. Goes (1970) studied the functional analytic properties of this space. The study of Hahn sequence space was initiated by Chandrasekhara Rao (1990) with certain specific purpose in the Banach space theory. In this paper, the matrix domain of the Hahn sequence space determined by the Cesáro mean first order, denoted by $C$, is obtained, and some inclusion relations and some topological properties of this space are investigated. Also dual spaces of this space are computed and, matrix transformations are characterized.