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Algebraic genericity and summability within the non-Archimedean setting

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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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Authors and Affiliations

  1. Department of Mathematics, University of Zanjan, Zanjan, 45371-38791, Iran

    J. Khodabandehlou & S. Maghsoudi

  2. Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), Universidad Complutense de Madrid, Plaza de Ciencias 3, Madrid, 28040, Spain

    J. B. Seoane-Sepúlveda

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  1. J. Khodabandehlou
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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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