Geodesic
Summability of Matrix Transforms of Subsequences
Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 359-364

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D. 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. 
Keagy, Thomas A. Summability of Matrix Transforms of Subsequences. Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 359-364. doi: 10.4153/CMB-1981-054-2
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     title = {Summability of {Matrix} {Transforms} of {Subsequences}},
     journal = {Canadian mathematical bulletin},
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     year = {1981},
     volume = {24},
     number = {3},
     doi = {10.4153/CMB-1981-054-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-054-2/}
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