A propriedade positiva de Schur em reticulados de Banach - Tabares, Juan David Rubio (2024)
The purpose of this dissertation is to study, in several aspects, the positive Schur property in Banach lattices. In order to justify the example of a Banach lattice with the positive Schur property failing the Schur property, a criterion for weak convergence in L 1 [0, 1], which recovers the Rademacher sequence as a particular instance, is proved. Examples, counterexamples and several properties of the positive Schur property are provided. We also study this property in countable direct sums and in l p (Γ)-spaces. Next, the positive Schur property in spaces of regular operators is investigated, and a lattice version of Ryan’s Theorem is proved. Finally, several characterizations of the positive Schur property in dual lattices are proved.