Isometries in Banach spaces: Lipschitz free spaces and topological properties

• Grant number: 10/00547-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: May 02, 2010
• End date: May 14, 2010
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Valentin Raphael Henri Ferenczi
• Visiting researcher: Gilles Godefroy
• Visiting researcher institution: Université Pierre et Marie Curie (Paris 6), France
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Professor Godefroy will visit the IME everyday for two weeks. During this period, he will give three mini-courses, addressed to post-graduation students, and a conference in the Coloquium of Mathematics of the Institute.He will also develop the following research program, in collaboration with Valentin Ferenczi.In the first direction of research, we shall study the Lipschitz free space F(M), that is the canonical predual of the space of Lipschitz functions on a metric space M, em certain specific cases. We shall study universality properties of F(U) where U is Urysohn space, in relation to other universal spaces. We shall also study the relations between F(l_1) and its bidual, to study whether every space Lispchitz isomorfic to l1 must be linearly isomorfic to l1.In a second direction, we shall study the problem of representability of a given group on a given Banach space, or more precisely, of a group G of isomorphisms on a space X as the group of isometries on X in some equivalent norm. We shall study to what degree a sufficient condition of representability proved by Ferenczi is necessary. (AU)