Domain of the double sequential band matrix in the classical sequence spaces

Let. denote any one of the classical spaces iota(infinity), c, c(0) and iota(p) of bounded, convergent, null and absolutely p- summable sequences, respectively, and lambda also be the domain of the double sequential band matrix B(r,s) in the sequence space lambda, where (r(n))(infinity)(n = 0) and (s(n))(infinity) (n = 0) are given convergent sequences of positive real numbers and 1 <= p <infinity. The present paper is devoted to studying the sequence space lambda. Furthermore, the beta- and gamma-duals of the space lambda. are determined, the Schauder bases for the spaces c, c(0) and iota(p) are given, and some topological properties of the spaces c(0), iota(1), and iota(p)are examined. Finally, the classes ( lambda(1) : lambda(2)) and ( lambda(1) : lambda(2)) of infinite matrices are characterized, where.lambda(1) epsilon {iota(infinity), c, c(0), iota(p), iota(1)} and lambda(2) {iota(infinity), c, c(0), iota(1)}.