Extensões ideais de classes de operadores multilineares e polinômios homogêneos entre espaços de Banach

• Autor(a) principal: Silva, Aluízio Antonio Fernandes da
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/21480; http://dx.doi.org/10.14393/ufu.di.2018.163
• topic: Espaços de Banach; Ideais de operadores multilineares e de polinômios homogêneos; Teorema de extensão; Operadores multilineares e polinômios homogêneos quase-$\tau$ (p)- somantes; Operadores multilineares e polinômios homogêneos sequencialmente w$^*$-compactos; Banach spaces; Ideals of multilinear operators and homogeneous polynomials; Quasi-$\tau (p)$-summing multilinear operators and homogeneous polynomials; Sequentially $w^{*}$-compact multilinear operators and homogeneous polynomials; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL

The main goal of this work is to establish necessary and su cient conditions for a class of continuous multilinear operators taking values in Banach spaces belonging to a certain class to be extendible to an ideal of multilinear operators (multi-ideal) and, moreover, to show how to extend an extendible class. Three applications of this extension result are provided: (i) It is proved that the class of quasi- (p)-summing multilinear operators taking values in dual spaces is extendible if and only if this class coincides isometrically with the class of (p)-summing multilinear operators; (ii) Starting with an ideal of (n + 1)-linear functionals, we construct an ideal of n-linear operators and study the main properties of the resulting ideal; (iii) The class of w -sequentially compact multilinear operators taking values in dual spaces is proved not to be extendible to a multi-ideal. Finally, almost the same de nitions, results and proofs are obtained for the case of classes of continuous homogeneous polynomials.