Rigidity of group action on Banach spaces

Specialeforsvar ved Emilie Mai Elkiær

Titel: Rigidity of group actions on Banach spaces 


Abstract: Kazhdan’s Property (T) is a fundamental notion in the study of groups and has applica-tions in a number of different fields of mathematics. It is initially defined in terms of unitary representations on Hilbert spaces, but was shown to be equivalent with a fixed-point property for affine actions of the group on Hilbert spaces. In this thesis, we study fixed-point and rigidity properties in the broader context of actions of groups on Banach spaces. We study the relations between two such properties for group actions on Lp -spaces – a class of Banach spaces where many of the tools from the study of actions on Hilbert spaces also applies. Furthermore, we study spectral conditions for Property (T) and for the related fixed-point property for actions on Lp -spaces.



Vejleder: Magdalena Musat
Censor:    David Kyed, SDU