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

Let lambda denote any one of the classical spaces l(infinity), c, c(0) and l(p) of bounded, convergent, null and absolutely p-summable sequences, respectively, and (lambda) over cap. also be the domain of the generalized difference matrix B(r, s) in the sequence space lambda, where 1 <= p < infinity. The present paper is devoted to studying on the sequence space A. Furthermore, the beta- and gamma-duals of the space <(lambda)over cap> are determined, and the Schauder bases for the spaces (c) over cap, (C-0) over cap and (l(p)) over cap are given, and some topological properties of the spaces (c(0)) over cap, (l(1)) over cap and (l(p)) over cap are examined. Finally, the classes ((lambda(1)) over cap, : lambda(2)) and ((lambda(1)) over cap : (lambda(2)) over cap) 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)). Published by Elsevier Ltd