International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2647-2653
doi:10.1155/IJMMS.2005.2647

Matrix transformations and Walsh's equiconvergence theorem

Abstract

In 1977, Jacob defines Gα, for any 0≤α<∞, as the set of all complex sequences x such that |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.