Tópicos em análise functional

• 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 the 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, demonstrate the Riesz representation theorem and the Hahn-Banach theorem, and finally, accomplish some applications.(AU)