Tipos de holomorfia em Espaços de Banach

• Autor(a) principal: Torres, Leodan Acuña
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/16817; https://doi.org/10.14393/ufu.di.2014.530
• topic: Espaços de Banach; Polinômios homogêneos contínuos; Função holomorfa; Tipo de holomorfia; Diferenciação de tipos de holomorfia; Ideais de polinômios homogêneos contínuos; Banach, Álgebra de; Polinômios; Banach spaces; Continuous homogeneous polynomials; Holomorphic function; Holomorphy types; Differentiation of holomorphy types; Ideals of continuous homogeneous polynomials; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The main purpose of this dissertation is to study the theory of holomorphy types between Banach spaces, mainly the differentiation of holomorphy types and the interplay between holomorphy types and ideals of homogeneous polynomials. To do so we first study continuous multilinear mappings and homogeneous polynomials between Banach spaces. Then we define and give examples of holomorphy types. Next we study the differentiation of holomorphy types as a method to generate new holomorphy types from a given one and we brie y study holomorphic functions associated to a given holomorphy type. Finally we show that every Banach ideal of homogeneous polynomials with property (B) is a holomorphy type and that, in the complex case, a closed ideal of polynomials is a holomorphy type if and only if it has property (B). We finish the work proving that, surprisingly, in the real case no closed ideal of polynomials has property (B).