Introdução à teoria dos reticulados de banach e operadores regulares

Abstract

The work presents a systematic introduction to the Theory of Banach lattices and to the study of Regular Operators defined on these spaces. Initially, the theoretical foundations are developed, focusing on Riesz spaces, Banach lattices, and the fundamental properties that connect the order structure with the normed space structure. The discussion then turns to operator theory, emphasizing positive operators and, in particular, regular ones. The investigation shows how the notion of regular operators is deeply connected to that of order-bounded operators, highlighting the importance of the Riesz–Kantorovich Theorem in establishing conditions of equivalence between these classes. Continuity and decomposition properties are also explored, as well as the construction of the so-called r-norm, which endows the space of regular operators with the structure of a Banach lattice under appropriate conditions.