Audrey Fovelle (Institute of Mathematics (IMAG) and Department of Mathematical Analysis, University of Granada) : On asymptotic B-convexity and linear types
Résumé : After defining the missing notions, we will see how a famous theorem of the local theory can be generalized in an asymptotic setting. More precisely, we will prove that a Banach space $X$ is asymptotically B-convex iff $ell_1$ is not asymptotically finitely representable in $X$ iff $X$ has nontrivial asymptotic infratype iff $X$ has nontrivial asymptotic Rademacher type iff $X$ has nontrivial asymptotic stable type.