Envelopes and ultrahomogeneity in Banach spaces

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)