Mathematical logic seminar - Nov 19 2019

Time: 3:30pm - 4:30 pm

Room: Wean Hall 8220

Speaker:     Valentin Ferenczi    
University of São Paulo

Title: Fraïssé and Ramsey properties of Lebesgue Lp spaces

Abstract:

We study the dynamics of the group of linear isometries of Lp-spaces. We define the central notion of a Fraïssé Banach space, showing that separable examples of this property are the spaces Lp(0,1) p ≠ 4,6,8 … (and the Gurarij space). In particular, we study the canonical actions of the isometry group of Lp(0,1) on the spaces of δ-isometric embeddings of finite dimensional subspaces of Lp(0,1) into itself, and we show that for p ≠ 4,6,8 … they are ε-transitive provided that δ is small enough. This extends the classical equimeasurability principle of Plotkin and Rudin. If time allows, we shall relate these results to a Ramsey property of the classes lpn, p ≠ 2, ∞.