Convex-transitivity and function spaces

It is shown that if X is it convex-transitive Banach space and 1 <= p < infinity, then L-p([0, 1], X) and L-s(infinity)([0, 1], X) are convex-transitive. Here L-s(infinity)([0, 1], X) is the closed linear span of the simple functions in the Bochner space L-infinity([0, 1], X). If H is all 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. (C) 2008 Elsevier Inc. All rights reserved.