arXiv subjects
Publications and source records attributed to Fabrício Santos.
In this paper, we explore the concept of multilinear operators that are multiple almost summing and present a new concept of type and cotype of multilinear operators and investigate the conditions for this new concept to recover the original concept of type and type for multilinear operators. We also show that these classes are Banach multi-ideals and establish the coherence and compatibility of these classes with the generated homogeneous polynomials.
In this paper we introduce a new approach to the concept of multipolynomials and generalize several results of the homogeneous polynomials and symmetric multilinear applications. We also present an abstract approach to the concept of absolutely summing multipolynomials
In this work we present a definition for coherence and compatibility of multilinear mappings and homogenous polynomial classes. These definitions are more restricted than the ones proposed before. We began analyzing this new definition in a technical sense, searching for what it has in common with other approaches. Then, we moved on to a more practical analysis. Through numerous examples of different classes of multilinear mappings and homogenous polynomials we checked the limits on these proposed definitions and propose there is a vast field in which they apply.
In this paper we provide an abstract aproach to the study of classes of multiple summing multilinear operators between Banach spaces. The main purpose is unify the study of several known classes and results, for example multiple $(p, q_1,\dots, q_n)$-summing operators, multiple mixing $(s, q, p)$-summing operators and multiple strong $(s, q, p)$-mixing summing operators. We also define new class of multiple summing multilinear operator that are particular cases of our construction and, therefore, satisfy the results proved in the paper.
In this paper, we construct the abstract ideal of polynomials. We show this is an ideal of Banach and, in a second moment, we explore the question of the coherence and compatibility of the pair composed by the abstract ideals of polynomials and multilinear applications.