On large ℓ₁-sums of Lipschitz-free spaces and applications

We prove that the Lipschitz-free space over a Banach space X X of density κ κ , denoted by F ( X ) F(X) , is linearly isomorphic to its ℓ 1 _1 -sum ( ⨁ κ F ( X ) ) ℓ 1 ( κF(X) )_1 . 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 0 over a L p L_p -space. More precisely, we establish that, for every 1 ≤ p ≤ ∞ 1≤ p≤ ∞ , if X X is a L p L_p -space of density κ κ , then L <mml:mi math