Sobre as extensões multilineares dos operadores absolutamente sonantes.

Abstract

In this work we study two generalizations of the well-known concept of absolutely summing operators. The first one consists of the multiple summing multilinear operators and it is focused on a result of coincidence that is equivalent to the Bohnenblust-Hille inequality. This inequality asserts that, for K = ℝ or ℂ and every positive integer m there exists positive scalars BK,m ≥ 1 such that, for every m-linear mapping U : KN×⋅ ⋅ ⋅×KN → K and every positive integer N, where (ei)Ni=1 denotes the canonical basis of KN. In this line our main goal is the investigation of the best constants BK,m satisfying the above inequality. The second generalization involves the concept of absolutely summing multilinear operators at a given point; we present an abstract version of these operators involving many of their properties. We prove that, considering appropriate sequence spaces, we have other kind of operators as particular cases of our version.