Matrix transformations and Walsh's equiconvergence theorem

In 1977, Jacob defines Gα, for any 0 ≤ α <∞, as the set of all complex sequences x such that limsup|xk|1/k ≤ α. In this paper, we apply Gu −Gv 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 Gu −Gv matrix transformation of the difference converges to zero in an arbitrarily large disk. Also, we give examples of such matrices.