Uniform homeomorphisms in interpolation scales of Banach spaces families

• Grant number: 23/07557-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: December 01, 2023
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Giulia Cardoso Fantato
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 23/18060-1 - Interpolation of families of Banach lattices and uniform homeomorphisms of spheres, BE.EP.DR

Abstract

The project involves the extension of techniques from a result by Daher, in the paper "Homéomorphismes uniformes entre les sphères unité des espaces d'interpolation", on the interpolation scale between two uniformly convex spaces.It is intended to extend Daher's techniques to the case of interpolation of a family of Banach spaces. The expected result is the existence of uniform homeomorphisms between spaces in the interior of the interpolation domain. Later, we expect to apply this result to prove that the sphere of Ferenczi's uniformly convex hereditarily indecomposable space, described in the paper "A uniformly convex hereditarily indecomposable Banach space", is uniformly homeomorphic to the sphere of the Hilbert space, obtaining the first known example of a hereditarily indecomposable space with this property.