On subspaces of indecomposable Banach spaces

Piotr Koszmider (IMPAN, Warsaw)

Mar 18. 2025, 14:45 — 15:30

We investigate the class of  Banach spaces that can be subspaces of indecomposable Banach spaces of densities up to continuum showing that it includes all Banach spaces of such densities which do not admit $\ell_\infty$ as quotients. It remains open if every Banach space that does not contain a copy of $\ell_\infty$ is a subspace of an indecomposable Banach space. The constructed indecomposable Banach space including an appropriate Banach space $X$  is a subalgebra of the algebra $C(K)$, where $K$ is the Cech-Stone remainder of the cartesian product of the dual ball of $X$ and the euclidean plane. The results were obtainen together with Zdenek Silber.

 

Further Information
Venue:
ESI Boltzmann Lecture Hall
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)