Classical vs. non-Archimedean analysis: an approach via algebraic genericity
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 ana...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71538 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71538 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.64 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 Álgebra Análisis funcional y teoría de operadores Funciones (Matemáticas) 1201 Álgebra 1202 Análisis y Análisis Funcional |
| Sumario: | 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. |
|---|