The dual spaces of sets of difference sequences of order m and matrix transformations

Abstract

Let p = (pk}∞k=0be a bounded sequence of positive reals, m ∈ and u be s sequence of nonzero terms. If x = (xk}∞k=0is any sequence of complex numbers we write Δ(m)x for the sequence of the m-th order differences of x and Δ(m)uX = {x = (x}∞k=0:uΔ(m)x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δ(m)uX for X = c0(p), c(p), l∞(p) and characterize some matrix transformations between these spaces Δ(m)X. © Springer-Verlag Berlin Heidelberg 2007.