Uniform homeomorphisms between unit spheres of interpolation spaces

• Ano de defesa: 2020
• Autor(a) principal: Gesing, Rafaela
• 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: Banach lattices; Complex interpolation; Homeomorfismos uniformes entre esferas; Interpolação complexa; Reticulados de Banach; Uniform homeomorphisms between spheres
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-09092020-160421/

This dissertation aims to present a detailed study of the article \"Homéomorphismes uniformes entre les sphères unité des espaces dinterpolation\" by M. Daher (1995), where he shows that, under certain hypotheses, the unit spheres of two complex interpolation spaces are uniformly homeomorphic. With this goal in mind, essential concepts will be addressed, among them, first, the theory where the results investigated are developed: theory of uniformly convex spaces, Bochner integral, and the Complex Interpolation Method of A. Calderón. Following, we present applications on the study of uniform homeomorphisms between unit spheres of Banach spaces on the interpolation scale, including the context of Lp spaces and weighted Lp spaces. Finally, we introduce some topics on the theory of Banach lattices and its interplay with interpolation theory, presenting the Calderón-Lozanovskii construction and the uniform homeomorphism between unit spheres in this setting.