The Banach-Saks rank of a separable weakly compact set

Victor Olmos Prieto (UNED)

Mar 20. 2025, 11:45 — 12:05

A well-known result by S. Banach and S. Saks states that every bounded sequence in $L^p([0,1])$, $1 < p < \infty$, has a Cesàro convergent subsequence. By taking the average of the subsequence multiple times, and through a recursive procedure, one can define a transfinite sequence of properties, thus giving rise to an ordinal rank or index for certain subsets of Banach spaces. We explore a different approach to this rank in the separable case using uniform families of finite subsets of integers. This allows us to characterize the existence of such a rank and study some of its properties from the point of view of Descriptive Set Theory.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Structures in Banach Spaces (Workshop)
Organizer(s):
Antonio Aviles (U Murcia)
Vera Fischer (U of Vienna)
Grzegorz Plebanek (U of Wroclaw)
Damian Sobota (U of Vienna)