Envelopes and ultrahomogeneity in Banach spaces

• Grant number: 22/04745-0
• Support Opportunities: Scholarships abroad - Research
• Start date: August 01, 2023
• End date: January 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Host Investigator: Jorge López-Abad
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Universidad Nacional de Educación a Distancia (UNED), Spain

Abstract

This is a project of research abroad (BPE) with professor J. Lopez-Abad, in Universidad Nacional de Educación a Distancia, Madrid, Espanha. The project will be concentrated on the study of a conjecture due V. Ferenczi, J. Lopez Abad, B. Mbombo, S. Todorcevic (2020): every separable Fraissé Banach space must be isometric to the Gurarij space or to some Lebesgue space Lp. Towards this conjecture, the following will be studied: envelopes in Banach spaces, especially envelopes in the Gurarij spaces, envelopes of the Hilbert space inside reflexive Fraïssé spaces, and renormings of Lebesgue Lp spaces in relation with Mazur rotation problem. (AU)