On the polynomial numerical index of the real spaces c0, 1 and ∞

We give a lower bound for the polynomial numerical index of order k for real lush spaces. We use this bound to compute the polynomial numerical index of order 2 of the real spaces c0, 1 and ∞. Finally, we present an example of a real Banach space X whose polynomial numerical indices are positive while the ones of its bidual are zero. © 2007 Elsevier Inc. All rights reserved