Topics in Functional Analysis

• Grant number: 12/15162-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2012
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Cristiano dos Santos
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project is intended to introduce the normed spaces, present some differences between finite dimensional spaces and infinite, study summability in case of normed spaces and Banach spaces, characterize the compact sets in the space of continuous functions by Arzela-Theorem Ascoli. In addition, we will study the Hilbert spaces and properties, we demonstrate the Riesz representation theorem and the Hahn-Banach theorem and finally accomplish some applications.