Professor Valentin Ferenczi
Professor, Department of Mathematics, University of São Paulo

Bio: Professor Valentin Ferenczi graduated from Ecole Polytechnique (1992), Paris, France, with a specialization in mathematics and economics; Ph.D. in Functional Analysis - Université Panthéon-Sorbonne (1995); and Habilitation à diriger des recherches in Mathematics - Université Pierre et Marie Curie (2009); Maître de Conférences at Université Pierre et Marie Curie since 1996. Since 2008, he is a full professor at the University of São Paulo, where he is responsible for the FAPESP Thematic Project "Geometry of Banach Spaces", and co-organized the "Brazilian Workshop in Geometry of Banach Spaces" conferences in 2014 and 2018. 

His area of research is Geometry of Banach spaces. Over the years he has also investigated its interactions with other areas such as: descriptive set theory, combinatorics and Ramsey theorems, group representations, homology, and Fraïssé theory.

Abstract: Joint work with J. Lopez-Abad, UNED Madrid.

We introduce the notion of isometric envelope of a subspace in a Banach space, establishing its connections with several key elements : (a) the mean ergodic projection on fixed points within a semigroup of contractions, (b) Korovkin sets from the 1970s, (c) extension properties of linear isometric embeddings. We use this concept to address recent conjectures on multilinear versions of Mazur rotation problem for separable Banach spaces. We characterize the Hilbert space as the only separable reflexive space in which any closed subspace coincides with its envelope; and we show that the Gurarij space satisfies the same property. We compute some envelopes in the case of the Lebesgue spaces Lp, and also identify the isometrically unique “full” quotient space of Lp by a Hilbertian subspace, for appropriate values of p, as well as the associated topological group embedding of the unitary group into the isometry group of Lp.