Lie algebras of linear operators on locally convex spaces
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 estab...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Brasil |
| Recursos: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-10102019-031720 |
| Acesso em linha: | http://www.teses.usp.br/teses/disponiveis/45/45132/tde-10102019-031720/ |
| Access Level: | acceso abierto |
| Palavra-chave: | 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 |
| Resumo: | 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. |
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