Matrix transformations of double sequences

Abstract

We study the space C_e of double sequences (x_kl) satisfying lim_l lim_k |x_kl-a| = 0 for some number a, and its subspace C_be of elements with bounded columns. Using the gliding hump method, we find necessary and sufficient conditions for a 4-dimensional matrix to transform a space X into a space Y, where X,Y ∈ {C_e,C_be}.