Mathematics (Sep 2019)
Orlicz–Pettis Theorem through Summability Methods
Abstract
This paper unifies several versions of the Orlicz−Pettis theorem that incorporate summability methods. We show that a series is unconditionally convergent if and only if the series is weakly subseries convergent with respect to a regular linear summability method. This includes results using matrix summability, statistical convergence with respect to an ideal, and other variations of summability methods.
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