Group Actions on Banach Spaces

Abstract

We survey the recent developments concerning fixed point properties for group actions on Banach spaces. In the setting of Hilbert spaces such fixed point properties correspond to Kazhdan's property (T). Here we focus on the general, non-Hilbert case, we discuss the methods, examples and several applications.

To appear in the "Handbook of Group Actions", ed.: L. Ji, A. Papadopoulos, S.-T. Yau

References in corpus (3)

• Strong property (T) for higher rank simple Lie groups
• Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces
• Automorphism groups of simplicial complexes and rigidity for uniformly bounded representations

Cited by in corpus (5)

• Sp(n,1) admits a proper 1-cocycle for a uniformly bounded representation
• Fixed-point spectrum for group actions by affine isometries on Lp-spaces
• Almost invariant CND kernels and proper uniformly Lipschitz actions on subspaces of $L^1$
• Wreath products of groups acting with bounded orbits
• Spaces with labelled partitions and isometric affine actions on Banach spaces