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

Let lambda denote any of the classical spaces l(infinity), c, c(0), and l(p) of bounded, convergent, null, and absolutely p-summable sequences, respectively, and let lambda(B) also be the domain of the triple band matrix B(r, s, t) in the sequence space lambda, where 1 < p < infinity. The present paper is devoted to studying the sequence space lambda(B). Furthermore, the beta- and gamma-duals of the space lambda(B) are determined, the Schauder bases for the spaces c(B),c(0)(B), and l(p)(B) are given, and some topological properties of the spaces c(0)(B), l(1)(B), and l(p)(B) are examined. Finally, the classes (lambda(1)(B) : lambda(2)) and (lambda(1)(B) : lambda(2)(B)) of infinite matrices are characterized, where lambda(1) is an element of {l(infinity), c, c(0), l(p), l(1)} and lambda(2) is an element of {l(infinity), c, c(0), l(1)}. (C) 2011 Elsevier Ltd. All rights reserved.