Algebraic genericity and summability within the non-Archimedean setting

In this paper, we establish the analogue of some recent lineability and algebrability results on the sets of sequences and series within the context of p -adic analysis. More specifically, we prove (among several other results) that: (i) in the space of all p -adic sequences, the set of all convergent sequences for which Cesàro’s Theorem fails is lineable, (ii) the set of all non-absolutely convergent p -adic series considered with Cauchy product or pointwise product is algebrable in c 0 .