Lie algebras of linear operators on locally convex spaces

• Ano de defesa: 2019
• Autor(a) principal: Cabral, Rodrigo Augusto Higo Mafra
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Álgebras de Lie; Álgebras localmente C*; Álgebras localmente convexas; Automorfismos; Automorphisms; Derivações; Derivations; Espaços localmente convexos; Exponenciação; Exponentiation; Grupos de Lie; Inverse limits; Lie algebras; Lie groups; Limites inversos; Limites projetivos; LMC*-algebras; Locally C*-algebras; Locally convex algebras; Locally convex spaces; Operadores pseudo-diferenciais; pro-C*-algebras; Projective analytic vectors; Projective limits; Pseudodifferential operators; Representações fortemente contínuas; Strongly continuous representations; Vetores analíticos projetivos
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/45/45132/tde-10102019-031720/

Necessary and sufficient conditions for the exponentiation of finite-dimensional real Lie algebras of linear operators on complete Hausdorff locally convex spaces are obtained, focused on the equicontinuous case - in particular, necessary conditions for exponentiation to compact Lie groups are established. Applications to complete locally convex algebras, with special attention to locally C*-algebras, are given. The definition of a projective analytic vector is given, playing an important role in some of the exponentiation theorems and in the characterization of the generators of a certain class of strongly continuous one-parameter groups.