On the Paranormed Nörlund Sequence Space of Nonabsolute Type

Abstract EN

Maddox defined the space ℓ ( p ) of the sequences x = ( x k ) such that ∑ k = 0 ∞ | x k | p k < ∞ , 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 ℓ ( 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 ) : μ ) and ( μ : N t ( p ) ) of infinite matrices are characterized.

Finally, some geometric properties of the space N t ( p ) are investigated.