DSpace Coleção: PAPGM

Normas tensoriais do tipo injetiva, propriedade de Dunford-Pettis e espaçabilidade no ambiente de classes de sequências

Tue, 24 Feb 2026 00:00:00 GMT

Título: Normas tensoriais do tipo injetiva, propriedade de Dunford-Pettis e espaçabilidade no ambiente de classes de sequências Autor(es): Sousa, Luiz Felipe de Pinho Orientador: Campos, Jamilson Ramos Abstract: In this work, we develop and expand the scope of the abstract environment based on the concept of sequence classes in three directions: in the theory of tensor norms and integral-type bilinear forms, in the direction of Dunford-Pettis type properties, and in the direction of spaceability in the context of sequence spaces and classes of linear operators. In the first part of the work, we study some classes of injective-type norms for the tensor product and the duality of these spaces, from which arises the definition of an integral-type bilinear form and a characterization for a certain sequence space. We also define and study a new concept of sequence class, called B-class, and present a generalization of the Dunford-Pettis property to Banach spaces. In the second part, we define and study the concept of standard sequence class, inspired by the concept of sequence class, with which we investigate notions of spaceability in the environments of (differences between) quasi-Banach sequence spaces and classes of linear operators. Editor: Universidade Federal da Paraíba Tipo: Tese

A search for linearity in the universe of topological vector spaces

Wed, 24 Jul 2024 00:00:00 GMT

Título: A search for linearity in the universe of topological vector spaces Autor(es): Ribeiro, Geivison dos Santos Orientador: Pellegrino, Daniel Marinho Abstract: This thesis provides criteria (both negative and positive) that contribute to the existing literature and address open problems within the notions of (α, β)-lineability/spaceability, (α, β)-dense lineability, pointwise lineability, and [S]-lineability. In our exploration, we began by investigating the behavior of algebraic and topological structures present in the set of unbounded, continuous, and integrable functions on the interval [0, ∞). This investigation was initiated by Calderón-Moreno, Gerlach-Mena, and Prado-Bassas, where they demonstrated, among other results, that the set A := f ∈ C [0, ∞) ∩ L1 [0, ∞) : lim sup x→∞ |f (x)| = ∞ is lineable. To better understand the dimensional relationships in this environment, we employed new techniques and gained additional insights into both the topological and algebraic structure of this set. Specifically, we proved its pointwise spaceability (and thus, spaceability). Additionally, we demonstrated that the set Lp[0, 1] \ S q∈(p,∞)Lq[0, 1], para p ∈ (0, ∞), although (1,c)-spaceable (see [21]), is not (א0,c)-spaceable. We established a general criterion for negative results concerning (α, β)-spaceability and verified that the set N D[0, 1] of nowhere differentiable functions cannot be (α, β)-spaceable for any infinite cardinal α. We also provided criteria for positive results, showing in particular that the sets l∞ \ F, where F ∈ {c, c0}, and Lp[0, 1] \ S q∈(p,∞)Lq[0, 1], for p ∈ (0, ∞), are (α,c)-espaceable if and only if α is finite. We introduced the notion of (α, β)-dense lineability and provided a criterion to demonstrate in particular that the set Lp[0, 1] \ S q∈(p,∞)Lq[0, 1], for p ∈ (0, ∞) is (α, β)- dense lineable for every 0 ≤ α ≤ β and max {α, א0} ≤ β ≤ c. Our findings highlight that the geometry of the studied sets alone is insufficient and that the type of topology considered in each environment also plays a crucial role. Editor: Universidade Federal da Paraíba Tipo: Tese

Sombreamento e estabilidade estrutural forte em Dinâmica Linear

Tue, 29 Jul 2025 00:00:00 GMT

Título: Sombreamento e estabilidade estrutural forte em Dinâmica Linear Autor(es): Azevedo, Mateus Vinicius Santos de Orientador: Costa Júnior, Fernando Vieira Abstract: In this work, we present the class of hyperbolic operators and their connection with the well-established concepts of shadowing and strong structural stability in discrete dynamical systems and ergodic theory. We then examine a characterization of weighted shift operators on c0 or ℓp spaces (where 1 ≤ p < ∞) satisfying the shadowing property, as demonstrated by N. C. Bernardes Jr. and A. Messaoudi (2020). Furthermore, we analyze how F. Bayart (2021) established that, in this framework, the shadowing property is equivalent to strong structural stability. Editor: Universidade Federal da Paraíba Tipo: Dissertação

Applications of geometric identities to rigidity problems

Fri, 21 Feb 2025 00:00:00 GMT

Título: Applications of geometric identities to rigidity problems Autor(es): Araújo, Murilo Chavedar de Souza Orientador: Freitas, Allan George de Carvalho Abstract: In this thesis, we explore the applications of integral identities, such as the Reilly-type and Pohozaev-type identities, in various geometric contexts, highlighting their roles in obtaining inequalities and rigidity results for specific classes of Riemannian manifolds. First, we consider the context of V -static manifolds, which are Riemannian manifolds with boundary, constant scalar curvature, and a metric that is a critical point of the volume functional with a fixed boundary metric. In this context, we employ our Reilly-type identity to establish Heintze-Karcher and Minkowski inequalities for bounded domains. Furthermore, we examine the rigidity phenomena associated with these inequalities, especially in cases where equality is achieved, shedding light on the geometric structure of these manifolds. Additionally, we obtain an inequality for domains in m-quasi Einstein manifolds along with a rigidity characterization. This inequality is motivated by the stability of the Wang-Yau energy. Finally, we turn our attention to weighted overdetermined problems on Riemannian manifolds with density. By studying a Poisson problem associated with the weighted Laplacian, we derive a Heintze-Karcher inequality and a Soap Bubble-type theorem that characterize geodesic balls in these weighted spaces. By imposing Dirichlet and Neumann boundary conditions, we also establish a Serrin-type result in generalized cones and convex cones of Euclidean space, identifying metric balls as the unique solutions to the underlying overdetermined problem. Editor: Universidade Federal da Paraíba Tipo: Tese