This is an announcement for the paper "Non-unitarisable representations and maximal symmetry" by Valentin Ferenczi and Christian Rosendal.
Abstract: We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique invariant complemented subspace. This is subsequently combined with rigidity results for the unitary representation of ${\rm Aut}(T)$ on $\ell_2(T)$, where $T$ is the countably infinite regular tree, to describe the possible bounded subgroups of ${\rm GL}(\mathcal H)$ extending a well-known non-unitarisable representation of $\mathbb F_\infty$. As a related result, we also show that a transitive norm on a separable Banach space must be strictly convex.
Archive classification: math.FA
Submitted from: rosendal.math@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1409.0141
or