Caracterização de compacidade fraca em espaços de Banach e sequências básicas em espaços localmente convexos

Abstract

In this thesis we will characterize weak-compactness of bounded, closed convex sets using some variations of the fixed point property. We will initially do this, in Banach spaces, using the Generic Fixed Point Property (G-FPP) for the class of affine bi-Lipschitz maps. Then introduce a relaxation of this notion (WG-FPP) and proved that a closed convex bounded subset of a Banach space is weakly compact iff it has the WG-FPP for affine 1-Lipschitz maps. We also explore the existence of basic sequences and almost-biorthogonal systems with topological constraints and some of their applications in the framework of locally convex spaces.