The isometry group of L^{p}(μ,\X) is SOT-contractible

Abstract

We will show that if (Ω,Σ,μ) is an atomless positive measure space, X is a Banach space and 1\leq p<\infty, then the group of isometric automorphisms on the Bochner space L^{p}(μ,X) is contractible in the strong operator topology. We do not require Σor X above to be separable.