Matrix transformations and Walsh's equiconvergence theorem

In 1977, Jacob definesGα, for any0≤α<∞, as the set of all complex sequencesxsuch that|xk|1/k≤α. In this paper, we applyGu−Gvmatrix 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 theGu−Gvmatrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.