MERCERIAN THEOREM FOR FOUR DIMENSIONAL MATRICES

Abstract

Let A = (ank)be an in...nite matrix and let c and cAbe the spaceof all convergent sequences with complex terms and convergence domain of A,respectively. In 1907, Mercer proved in [On the limits of real variants, Proc.London Math. Soc. 2 (1) (1907), no. 5, 206-224.] that c = cAwhich is calleda Mercerian theorem. In this paper, we give the corresponding theorem for afour dimensional matrix and the space of convergent double sequences in thePringsheim's sense.