Tipo e cotipo de espaços de Banach e espaços Lp de Banach / Type and cotype of Banach spaces and Lp-spaces




In this work we study two topics: the basic theory of type and cotype and the Lp-spaces theory. We show that each Lr -space, 1 · r <1; has type min fr; 2g and cotype max fr; 2g. We also prove that no infinite dimensional L1 -space can have type >1 and cotype <1. We detail the study of the Khintchine and Kahane inequalities, needed in order to have full understanding of the type, cotype theory. A chapter is dedicated to the study of generalizations of the Khintchine inequality (the classical Rademacher functions are replaced by the so called n-Rademacher functions). It is shown that if we use these n-Rademacher functions to define type and cotype, the new definitions are equivalent to the usual ones


functional analysis espaços banach spaces banach analise funcional

Documentos Relacionados