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The sequence spaces `∞(p), c(p) and c0(p) were introduced and studied by Maddox [Proc. Cambridge Philos. Soc. 64 (1968), 335–340]. In the present paper, we introduce the sequence spaces `∞(B, p), c(B, p) and c0(B, p) of non-absolute type which are derived by the triple band matrix B(r, s, t) and is proved that the spaces `∞(B, p), c(B, p) and c0(B, p) are paranorm isomorphic to the spaces `∞(p), c(p) and c0(p); respectively. Besides this, the α-, βand γ-duals of the spaces `∞(B, p), c(B, p) and c0(B, p) are computed and the bases of the spaces c(B, p) and c0(B, p) are constructed. Finally, the matrix mappings from the sequence spaces λ(B, p) to a given sequence space μ and from the sequence space μ to the sequence space λ(B, p) are characterized, where λ ∈ {`∞, c, c0}.

Domain of the triple band matrix on some Maddox's spaces