Some new sequence spaces derived by the domain of generalized difference matrix

Abstract

Let λ denote any one of the classical spaces ℓ ∞ , c , c 0 and ℓ p of bounded, convergent, null and absolutely p -summable sequences, respectively, and λ ̂ also be the domain of the generalized difference matrix B ( r , s ) in the sequence space λ , where 1 ≤ p < ∞ . The present paper is devoted to studying on the sequence space λ ̂ . Furthermore, the β - and γ -duals of the space λ ̂ are determined, and the Schauder bases for the spaces c ̂ , c ̂ 0 and ℓ ̂ p are given, and some topological properties of the spaces c ̂ 0 , ℓ ̂ 1 and ℓ ̂ p are examined. Finally, the classes ( λ ̂ 1 : λ 2 ) and ( λ ̂ 1 : λ ̂ 2 ) of infinite matrices are characterized, where λ 1 ∈ { ℓ ∞ , c , c 0 , ℓ p , ℓ 1 } and λ 2 ∈ { ℓ ∞ , c , c 0 , ℓ 1 } .