Title: A general criteria for a stronger notion of lineability

Abstract: A subset A of a vector space X is called α-lineable whenever A contains, except for the null vector, a subspace of dimension α. If X has a topology, then A is α-spaceable if such subspace can be chosen to be closed. The vast existing literature on these topics has shown that positive results for lineability and spaceability are quite common. Recently, the stricter notions of (α,β)-lineability/spaceability were introduced as an attempt to shed light to more subtle issues. In this talk, among other results, we present some general criteria for the notion of (α,β)-lineability/spaceability and, as applications, we extend recent results of different authors.

Title: Kitai’s Criterion for composition operators

Abstract: In this talk, we define some classes of chaoticity studied in Linear Dynamics. We present about composition operators acting on spaces of measurable functions. We then characterize composition operators satisfying Kitai’s Criterion and give an example of a composition operator that is mixing but does not satisfy Kitai’s Criterion. (This is a joint work with Karl-G. Grosse-Erdmann, from Université de Mons, Belgium).

Title: Injective type norms and integral bilinear forms defined by sequence classes

Abstract: In this work we define classes of injective norms for tensor products through the abstract environment of sequence classes. Examples and results on these norms will be presented and the dual of the tensor product will be constructed, when equipped with one of these norms. This dual leads us to the definition of a class of integral type bilinear forms.

Title: On B-classes and coincidence results in operator theory

Abstract: From a Banach space B and a sequence class X, we define a new sequence class, called the B-class, associated with X, which generalizes certain well-known vector-valued sequence spaces. In this talk, we will discuss examples and results related to B-classes, as well as a class of coincidence results in the theory of operator ideals.

Title: On multipolynomial extensions of Kahane-Salem-Zygmund inequality and applications

Abstract: Some classical and recent Kahane-Salem-Zygmund inequalities developed into several contexts are extended to multipolynomials. The study compares such extensions to each other to comprehend which of them yields the smallest norm for the associated function. Applications to the multilinear and polynomial scenarios are provided.

Title: Classes intermediárias de operadores multilineares nucleares.

Abstract: Nesta apresentação, abordaremos a classe de operadores m-lineares (p_1,…,p_m,σ,q,ν)-nucleares entre espaços de Banach, considerando-a como um espaço intermediário entre a classe de operadores m-lineares nucleares e a classe geral de operadores m-lineares limitados. Estabeleceremos conexões com a teoria de operadores m-lineares somantes. Além disso, identificaremos esse espaço com um espaço dual por meio de uma norma cruzada razoável, inspirada na norma de Chevet–Saphar.

Title: Bases de Schauder em determinados espaços de funções holomorfas

Abstract: Uma sequência (e_n) de um espaço localmente convexo E é uma base de Schauder para E se para todo x\in E existir uma única sequência de escalares (\alpha_n) tal que a série \sum^{\infty}_{n=1}\alpha_ne_n converge para x, e os funcionais coordenados x\mapsto \alpha_n são lineares e contínuos. Nesse sentido, vários autores provaram que alguns espaços de funções holomorfas com as topologias naturais possuem base de Schauder. Nesse encontro, vamos mostrar que alguns espaços do tipo c_0-somas e também o pré-dual do espaço de sequência de Lorentz d_*(w,1) possuem base de Schauder. Esse é um trabalho em conjunto com Mary Lilian Lourenço.

Title: Problemas em Aberto sobre o Espectro de Subespaços

Abstract: Nesta palestra, abordaremos questões fundamentais sobre o espectro oscilante de subespaços de funções, com foco em C[0,1] . Discutiremos problemas em aberto, como a caracterização completa do espectro, sua relação com subespaços complementados, sua densidade, enumerabilidade e condições que garantem sua finitude. Exploraremos também a interação do espectro no contexto dos operadores lineares contínuos. A palestra se baseará em resultados clássicos e recentes, incluindo o artigo Some Results and Open Questions on Spaceability in Function Spaces (Transactions of the American Mathematical Society, vol. 366, n. 2, 2014) de Enflo e colaboradores, e o artigo On the Existing Set of the Oscillating Spectrum, publicado em 2023 no Journal of Functional Analysis pela Elsevier, de autoria de Rui Xie.