Classical vs. non-Archimedean analysis: an approach via algebraic genericity

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Fernández Sánchez, J. and Maghsoudi, S. and Rodríguez-Vidanes, D.L. and Seoane Sepúlveda, Juan Benigno (2022) Classical vs. non-Archimedean analysis: an approach via algebraic genericity. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 116 (2). ISSN 1578-7303

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Official URL: https://doi.org/10.1007/s13398-022-01209-5



Abstract

In this paper, we show new results and improvements of the non-Archimedean counterpart of classical analysis in the theory of lineability. Besides analyzing the algebraic genericity of sets of functions having properties regarding continuity, discontinuity, Lipschitzianity, differentiability and analyticity, we also study the lineability of sets of sequences having properties concerning boundedness and convergence. In particular we show (among several other results) the algebraic genericity of: (i) functions that do not satisfy Liouville’s theorem, (ii) sequences that do not satisfy the classical theorem of Cèsaro, or (iii) functionals that do not satisfy the classical Hahn–Banach theorem.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:P-adic numbers; P-adic continuous function; P-adic differentiable function; P-adic sequences; Lineability; Algebrability; Spaceability; Cesàro summable; Non-absolutely convergent series; Liouville’s theorem; Lipschitz condition; Hahn–Banach theorem
Subjects:Sciences > Mathematics > Algebra
Sciences > Mathematics > Functional analysis and Operator theory
Sciences > Mathematics > Functions
ID Code:72536
Deposited On:27 May 2022 14:21
Last Modified:30 May 2022 07:07

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