Some new sequence spaces derived by the domain of the triple band matrix

Let λ denote any of the classical spaces ?_∞,c,c₀, and ?_p of bounded, convergent, null, and absolutely p-summable sequences, respectively, and let λ(B) also be the domain of the triple band matrix B(r,s,t) in the sequence space λ, where 1<p<∞. The present paper is devoted to studying the sequence space λ(B). Furthermore, the β- and γ-duals of the space λ(B) are determined, the Schauder bases for the spaces c(B), c₀(B), and ?_p(B) are given, and some topological properties of the spaces c₀(B), ?₁(B), and ?_p(B) are examined. Finally, the classes (λ₁(B):λ₂) and (λ₁(B):λ₂(B)) of infinite matrices are characterized, where λ₁∈{?_∞,c,c₀,?_p,?₁} and λ₂∈{?_∞,c,c₀,?₁}.