Matrix Summability of Statistically P-Convergence Sequences

Richard F. Patterson, Ekrem Savaş

Matrix summability is arguable the most important tool used to characterize sequence spaces. In 1993 Kolk presented such a characterization for statistically convergent sequence space using nonnegative regular matrix. The goal of this paper is extended Kolk's results to double sequence spaces via four dimensional matrix transformation. To accomplish this goal we begin by presenting the following multidimensional analog of Kolk's Theorem: Let $X$ be a section-closed double sequence space containing $e''$ and $Y$ an arbitrary sequence space. Then $B\in(st_A^2\cap X,Y)$ if and only if $B\in(c''\cap X,Y)$ and $B^{[K\times K]}\in(X,Y)(\delta_A(K\times K)=0)$. In addition, to this result we shall also present implication and variation of this theorem.