λ-Rearrangements Characterization of Pringsheim Limit Points

In [1] Agnew presented the following theorem: if x is a bounded sequence and A is a regular summability matrix, then there exists a subsequence y of x such that each limit point of x is a limit point of Ay. Fridy [2] extended this result by replacing subsequence with rearrangement. Keagy [3] presented two theorems that strengthened the results of both Agnew and Fridy. This was accomplished by weakening the regularity conditions and replacing finite limit point for bounded sequence. The goal of the paper is to present two multidimensional theorems analogou to Keagy’s theorems with λ-rearrangement replacing rearrangement, RH-regularity replacing regularity, and convergent in the Pringsheim sense replacing convergent. Other implications will also be presented.