The existence of affine isometric actions with unbounded orbits on Lp spaces: dependence on p

• Ano de defesa: 2023
• Autor(a) principal: Fantato, Giulia Cardoso
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Ações de grupos topológicos; Affine isometries; Espaços Lp; Isometrias afins; Lp-spaces; Topological group actions
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-13042023-111939/

The central direction of the study of this thesis is to detail a theorem and its corollaries from the recent paper \"Isometric actions on Lp-spaces: dependence on the value of p\" by Marrakchi and de la Salle (2020). These authors show that if a topological group G admits an affine isometric action with unbounded orbits on an Lp-space, then G admits the same type of action on Lq, for every q > p. In order to achieve that, we explore all the group actions needed, such as affine isometric actions, nonsingular actions and skew-product actions, examining the theory of cocycles. Additionally, we investigate the Banach-Lamperti theorem, which characterizes isometries on Lp, for p not equal to 2, and analyse its topological aspects. The case p=2 is treated with different tools, namely functions conditionally of negative type and the GNS construction.