A fixed point theorem for L^1 spaces

Abstract

We prove a fixed point theorem for a family of Banach spaces, notably L^1 and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the "derivation problem" studied since the 1960s.

minor additions; to appear in Inv. Math

References in corpus (1)

• Property (T) and rigidity for actions on Banach spaces

Cited by in corpus (14)

• Approximation properties for noncommutative $L^p$-spaces of high rank lattices and nonembeddability of expanders
• Strong Banach Property (T) for Simple Algebraic Groups of Higher Rank
• Random groups, random graphs and eigenvalues of p-Laplacians
• Towards Strong Banach property (T) for SL(3,R)
• Smooth bimodules and cohomology of II${}_1$ factors
• Acylindrically hyperbolic groups with exotic properties
• Isomorphisms between spaces of Lipschitz functions
• Banach space actions and $L^2$-spectral gap
• Fixed point theorems for metric spaces with a conical geodesic bicombing
• Superrigidity of actions on finite rank median spaces
• Applications of uniform asymptotic regularity to fixed point theorems
• Banach property (T) for $\mathrm{S}{\mathrm{L}}_{\mathrm{n}}(\mathbb{Z})$ and its applications
• Derivations and homomorphisms in commutator-simple algebras
• Around the nonlinear Ryll-Nardzewski theorem