Métodos para construir hiper-ideais de aplicações multilineares

Abstract

In this work, we study two methods proposed by G. Botelho and E. Torres, in 2017, to construct hyper-ideals of continuous multilinear applications: the limitation method and the inequality method. The first is an adaptation of what R. Aron and P. Rueda did, in 2012, for homogeneous polynomials. This method, like classical methods for constructing multi-ideals, generates hyper-ideals from the ideals of linear operators. Behaving differently, the second method studied is based on the transformation of finite vector-valued sequences by multilinear applications. Besides to generate new hyperideals, such methods can be used to show that known classes of continuous multilinear applications enjoy the property of hyper-ideal. In addition, we prove that the hyperideals obtained by them are related to the notion of coherence of multi-ideals.