Convergencia de series en espacios normados. Un estudio dirigido a los estudiantes de la carrera de Matemática de la ESPOCH

Abstract

The objective of this research project was to produce a monograph on the convergence of series in normed spaces, supported by existing and most outstanding bibliography. The methodology used in the development of this research work was based on a qualitative approach, with a descriptive scope and documentary in nature. This involved the search, collection, analysis, and compilation of information on the aforementioned topic, detailing various definitions of convergence of series in normed spaces, as well as identifying equivalences between these definitions. Special attention was given to the study of series convergence in Banach and Hilbert spaces, considering their particularities and distinctive properties. At the conclusion of this research, fundamental results were obtained that support the relevance and usefulness of the monograph named “Convergence of series in normed spaces”. It is expected that this work will significantly contribute to the education of new and current students of Mathematics at ESPOCH (Escuela Superior Politecnica de Chimborazo), providing them with a solid understanding of the conditions for series convergence and the various properties that these may exhibit. Ultimately, this monograph should serve as a valuable educational tool, facilitating the comprehension and application of advanced mathematical concepts in the field of normed spaces.