Abstract
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 \(c_0\).
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J. B. Seoane-Sepúlveda was supported by Grant PGC2018-097286-B-I00.
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Khodabandehlou, J., Maghsoudi, S. & Seoane-Sepúlveda, J.B. Algebraic genericity and summability within the non-Archimedean setting. RACSAM 115, 21 (2021). https://doi.org/10.1007/s13398-020-00961-w
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DOI: https://doi.org/10.1007/s13398-020-00961-w
Keywords
- p-adic numbers
- Lineability
- Non-absolutely convergent p-adic series
- p-adic sequences
- Algebrability
- Cesàro’s theorem
- Ratio and root tests