On the Paranormed Nörlund Sequence Space of Nonabsolute Type

Abstract

Maddox defined the space $\ell (p)$ of the sequences $x=(x_k)$ such that , in Maddox, 1967. In the present paper, the Nörlund sequence space $N^t(p)$ of nonabsolute type is introduced and proved that the spaces $N^t(p)$ and $\ell (p)$ are linearly isomorphic. Besides this, the alpha-, beta-, and gamma-duals of the space $N^t(p)$ are computed and the basis of the space $N^t(p)$ is constructed. The classes $(N^t(p):\mu )$ and $(\mu :N^t(p))$ of infinite matrices are characterized. Finally, some geometric properties of the space $N^t(p)$ are investigated.