Generalization of the sequence space [formula omitted] derived by weighted mean

Abstract

The sequence space ℓ ( p ) was introduced and studied by Maddox [I.J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford (2) 18 (1967) 345–355]. In the present paper, the sequence spaces ℓ ( u , v ; p ) of non-absolute type which is derived by the generalized weighted mean is defined and proved that the spaces ℓ ( u , v ; p ) and ℓ ( p ) are linearly isomorphic. Besides this, the β- and γ-duals of the space ℓ ( u , v ; p ) are computed and the basis of that space is constructed. Further, it is established that the sequence space ℓ p ( u , v ) has AD property and given f-dual of the space ℓ p ( u , v ) . Finally, the matrix mappings from the sequence spaces ℓ ( u , v ; p ) to the sequence space μ and from the sequence space μ to the sequence space ℓ ( u , v ; p ) are characterized.