On Some New Generalized Difference Sequence Spaces of Nonabsolute Type (original) (raw)

2014, Journal of Mathematics

We define a new triangle matrix̂= ( ) by the composition of the matrices Λ = ( ) and ( , , ). Also, we introduce the sequence spaces 0 (̂), (̂), ℓ ∞ (̂), and ℓ (̂) by using matrix domain of the matrix̂on the classical sequence spaces 0 , , ℓ ∞ , and ℓ , respectively, where 1 ≤ < ∞. Moreover, we show that the space (̂) is norm isomorphic to for ∈ { 0 , , ℓ ∞ , ℓ }. Furthermore, we establish some inclusion relations concerning those spaces and determine -, -, and -duals of those spaces and construct the Schauder bases 0 (̂), (̂), and ℓ (̂). Finally, we characterize the classes ( 1 (̂) : 2 ) of infinite matrices where 1 ∈ { , 0 , ℓ } and 2 ∈ {ℓ ∞ , , 0 , ℓ }.