Summability of Matrix Transforms of Subsequences

Abstract

AbstractD. F. Dawson has considered several questions of the following nature. Suppose T is a regular matrix summability method. If A is a regular matrix and x is a sequence having a finite limit point, then there exists a subsequence y of x such that each finite limit point of x is a T-limit point of Ay. In the present paper, we show the regularity condition for A may be replaced by the requirement that A be a limit preserving bv to c map. This leads to summability characterizations for several classes of sequences.