ON LARGE l1-SUMS OF LIPSCHITZ-FREE SPACES AND APPLICATIONS

. We prove that the Lipschitz-free space over a Banach space X of density kappa, denoted by F(X), is linearly isomorphic to its l(1)-sum (circle plus k F(X)).e1. This provides an extension of a previous result from Kaufmann in the context of non-separable Banach spaces. Further, we obtain a complete classification of the spaces of real-valued Lipschitz functions that vanish at 0 over a Lp-space. More precisely, we establish that, for every 1 <= p <= infinity, if X is a Lp-space of density kappa, then Lip(0)(X) is either isomorphic to Lip(0)(lp(kappa)) if p < infinity, or Lip(0)(c(0)(kappa)) if p = infinity.