A topologia Right em espaços de Banach e operadores pseudo fracamente compactos

Abstract

The Right topology was introduced by A. M. Peralta, I. Villanueva, J. D. Maitland Wright e K. Ylinen in 2007 as a topological tool to deepen the understanding of weakly compact operators on Banach spaces. Since then, this topology has played a relevant role in Banach space theory. The main purpose of this dissertation is to provide a detailed study of the Right topology on Banach spaces and its applications to the theory of pseudo weakly compact operators. We begin by gathering fundamental results in Functional Analysis and Banach space theory, such as weak convergence, compact operators, weakly compact operators and operator ideals. Next we introduce the Right topology and we investigate its basic properties, such as separation axioms, behavior with respect to subspaces and to product spaces, as well as its relationships with the norm topology and the weak topology. The next step is the investigation of (spaces of) Right null sequences and different sequence classes associated to them, establishing connections with classical properties. Finally, we study the class of pseudo weakly compact operators, providing definition, basic and fundamental properties, examples, counterexamples, and relations with operator ideals. Some open problems in the area are also discussed.