Matrix transformations and Walsh's equiconvergence theorem

In 1977, Jacob defines G_α, for any 0 ≤ α < ∞, as the set of all complex sequences x such that lim sup x_k ^1/k ≤ α. In this paper, we apply G_u - G_v matrix transformation on the sequences of operators given in the famous Walsh's equiconvergence theorem, where we have that the difference of two sequences of operators converges to zero in a disk. We show that the G_u - G_v matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.