The dual spaces of the sets of difference sequences of order m

Abstract

The idea of difference sequence spaces was introduced by Kizmaz 5 and the concept was generalized by Et and Çolak 3. Let p = (pk) be a bounded sequence of positive real numbers and v = (vk) be any fixed sequence of non-zero complex numbers. If x = (xk) is any sequence of complex numbers we write ?vmx for the sequence of the m -th order differences of x and ?vm(X) = {x = (xk) : ?vmx ? X} for any set X of sequences. In this paper we determine the ? -, ?- and ? - duals of the sets ?vm(X) which are defined by Et et al. 2 for X = ??(p), c(p) and c0(p). This study generalizes results of Malkowsky 9 in special cases. © 2006 Victoria University. All rights reserved.