Convex-transitivity and function spaces

It is shown that if X is a convex-transitive Banach space and 1 ⩽ p < ∞ , then L p ( [ 0 , 1 ] , X ) and L s ∞ ( [ 0 , 1 ] , X ) are convex-transitive. Here L s ∞ ( [ 0 , 1 ] , X ) is the closed linear span of the simple functions in the Bochner space L ∞ ( [ 0 , 1 ] , X ) . If H is an infinite-dimensional Hilbert space and C 0 ( L ) is convex-transitive, then C 0 ( L , H ) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces are provided.