The isometry group of Lp(μ,X) is SOT-contractible

We will show that if (Ω,Σ,μ) is an atomless positive measure space, X is a Banach space and 1⩽p<∞, then the group of isometric automorphisms on the Bochner space Lp(μ,X) is contractible in the strong operator topology. We do not require Σ or X above to be separable.