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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-05092016-143504
Document
Author
Full name
Ewerton Ribeiro Torres
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Botelho, Geraldo Márcio de Azevedo (President)
Ascui, Jorge Tulio Mujica
Fávaro, Vinícius Vieira
Pellegrino, Daniel Marinho
Vieira, Daniela Mariz Silva
Title in Portuguese
Hiper-ideais de aplicações multilineares e polinômios homogêneos em espaços de Banach
Keywords in Portuguese
Aplicações multilineares
Espaços de Banach
Hiper-ideais
Multi-ideais
Polinômios homogêneos
Abstract in Portuguese
Nesse trabalho introduzimos e desenvolvemos a teoria de hiper-ideais de aplicações multilineares contínuas e polinômios homogêneos contínuos entre espaços de Banach. A ideia central é refinar os conceitos de multi-ideais e de ideais de polinômios com o objetivo de explorar de forma mais aprofundada a natureza não-linear das aplicações envolvidas. Para isso tomamos a teoria de ideais de operadores lineares, aplicações multilineares e polinômios homogêneos, desenvolvida a partir dos trabalhos de Pietsch, tanto no caso linear como no caso multilinear, como referencial. Provamos resultados gerais para hiper-ideais, damos muitos exemplos ilustrativos, e desenvolvemos métodos para gerar hiper-ideais, tanto no caso multilinear como no caso polinomial.
Title in English
Hyper-Ideals of multilinear mappings and homogeneous polynomials in Banach spaces
Keywords in English
Banach spaces
Homogeneous polynomials
Hyper-ideals
Multiideals
Multilinear mappings
Abstract in English
In this work we introduce and develop the theory of hyper-ideals of multilinear mappings and homogeneous polynomials between Banach spaces. The main idea is to refine the concepts of multi-ideal and of ideal of polynomials with the purpose of exploring deeply the nonlinear nature of the underlying mappings. To do this we take the ideal theory of linear operators, multilinear mappings and homogeneous polynomials, developed from the works of Pietsch, both in the linear and nonlinear cases, as a reference. We prove general results for hyper-ideals, provide a number of illustrative examples, and develop methods to generate hyper-ideals of multilinear mappings, as well as of hyper-ideals of homogeneous polynomials.
 
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Publishing Date
2017-04-03
 
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