Existência e inexistência de subespaços frequentemente hipercíclicos para operadores weighted shifts

Abstract

In this dissertation, we study criteria for the existence and nonexistence of frequently hypercyclic subspaces. We begin by presenting classical results from functional analysis that are essential for the development of this study. Then, we discuss important properties related to the dynamics of hypercyclic operators, with emphasis on the Hypercyclicity Criterion. We also introduce the notions of frequently hypercyclic operators and frequently hypercyclic subspaces. The main goal of this work is to provide a detailed study of the results in [33], which establishes conditions for the existence and nonexistence of frequently hypercyclic subspaces for weighted shift operators. Finally, we construct examples of operators that satisfy these criteria.