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Doctoral Thesis
Full name
Rodrigo Augusto Higo Mafra Cabral
Knowledge Area
Date of Defense
São Paulo, 2019
Forger, Frank Michael (President)
Jakel, Christian Dieter
Júnior, Luiz Roberto Hartmann
Melo, Severino Toscano do Rego
Ribeiro, Pedro Lauridsen
Title in English
Lie algebras of linear operators on locally convex spaces
Keywords in English
Inverse limits
Lie algebras
Lie groups
Locally C*-algebras
Locally convex algebras
Locally convex spaces
Projective analytic vectors
Projective limits
Pseudodifferential operators
Strongly continuous representations
Abstract in English
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.
Title in Portuguese
Álgebras de Lie de operadores lineares em espaços localmente convexos
Keywords in Portuguese
Álgebras de Lie
Álgebras localmente C*
Álgebras localmente convexas
Espaços localmente convexos
Grupos de Lie
Limites inversos
Limites projetivos
Operadores pseudo-diferenciais
Representações fortemente contínuas
Vetores analíticos projetivos
Abstract in Portuguese
Condições necessárias e suficientes para a exponenciação de álgebras de Lie reais de dimensão finita de operadores lineares sobre espaços localmente convexos completos Hausdorff são obtidas, com foco no caso equicontínuo - em particular, condições necessárias para a exponenciação com respeito a grupos de Lie compactos são estabelecidas. Aplicações para álgebras localmente convexas completas são dadas, com uma atenção especial para álgebras localmente C*. A definição de vetor analítico projetivo é introduzida, possuindo um papel importante em alguns dos teoremas de exponenciação e na caracterização dos geradores de uma certa classe de grupos a um parâmetro fortemente contínuos.
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