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

Let λλ denote any one of the classical spaces ℓ∞ℓ∞, cc, c0c0 and ℓpℓp of bounded, convergent, null and absolutely pp-summable sequences, respectively, and λ̂ also be the domain of the generalized difference matrix B(r,s)B(r,s) in the sequence space λλ, where 1≤p<∞1≤p<∞. The present paper is devoted to studying on the sequence space λ̂. Furthermore, the ββ- and γγ-duals of the space λ̂ are determined, and the Schauder bases for the spaces ĉ, ĉ0 and ℓ̂p are given, and some topological properties of the spaces ĉ0, ℓ̂1 and ℓ̂p are examined. Finally, the classes (λ̂1:λ2) and (λ̂1:λ̂2) of infinite matrices are characterized, where λ1∈{ℓ∞,c,c0,ℓp,ℓ1}λ1∈{ℓ∞,c,c0,ℓp,ℓ1} and λ2∈{ℓ∞,c,c0,ℓ1}λ2∈{ℓ∞,c,c0,ℓ1}.