Cesàro Means of Subsequences of Double Sequences
DOI:
https://doi.org/10.5644/SJM.15.02.03Keywords:
Double sequences, Pringsheim convergence, the Buck-Pollard Property, double subsequencesAbstract
In this paper we characterize the convergence and $\left( C,1,1\right) $ summability of a double sequence. In particular we study conditions under which the convergence or $\left( C,1,1\right) $ summability of a double sequence carry over to that of its subsequences, \ and conversely, whether these properties for suitable subsequences imply them for the sequence itself. We show, for instance, that a bounded double sequence is $\left(C,1,1\right) $ summable if and only if almost all of its subsequences are $\left( C,1,1\right) $ summable.
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